Map from Google - Kazakhstan

Kazakhstan, a vast country of Central Asia, has a markedly continental climate, with very cold winters almost everywhere, while summers are warm in the north and definitely hot in the south. There are no obstacles which could protect the country from cold air masses of polar or Siberian origin, while in summer the hot winds from the deserts of Iran can blow. Central Asia becomes very cold in winter and very hot in summer, because of the huge distance from the oceans, so that both the highest and coldest records are noticeable: in the north the temperature can reach -50 °C (-58 °F) in winter, as well as 40 °C (104 °F) in summer, while in the south it can go from -35 °C (-31 °F) in winter to 45 °C (113 °F) in summer. Clashes between different air masses can give rise to strong winds and dust storms, especially in spring and in the south, while in winter, northern winds can cause blizzards, but without great snow accumulations, due to the scarcity of precipitation.
The distance from the sea is also the cause of the climate aridity, in fact, the country is almost entirely covered by steppes and deserts; the northern area (roughly above the 50th parallel) is the rainiest part, where precipitation exceeds 300 millimetres (12 inches) per year, mainly because of afternoon thunderstorms that occur in summer, while in the centre and south, it comes down to around 150/200 mm (6/8 in) per year, and even to around 100 mm (4 in) in the area of the Aral Sea. Snow, in the long winter months is quite common, but it's often light and not abundant. There are approximately a hundred days with snow each year on the plains in the far north (see Petropavl), about 60 days in the central region, and about 20 days in the southernmost part.
The mildest area in winter is the south-west, along the coast of the Caspian Sea, where the average in January goes from -6 °C (21 °F) in the northern coast (see Atyrau), to -2 °C (28 °F) in the east coast (see Aktau), to almost 0 °C (32 °F) near the border with Turkmenistan; there's also a small portion in the south-central part of the country, near the border with Uzbekistan, where the average is about freezing as well. In general, at a given latitude, the winter temperature decreases as you proceed towards the east.
Here are the average temperatures throughout Kazakhstan in January.

January average temperature in Kazakhstan

The summer temperatures are more uniform, and vary mainly depending on latitude, as well as on altitude (but most of the country is flat): in July, they range on average from 19 °C (66 °F) in the far north, to 25 °C (77 °F) in the centre-south, to nearly 30 °C (86 °F) in the far south.
As mentioned, even precipitation varies from north to south: the northern part, the rainiest, is occupied by the Kazakh steppe (or Kirghiz steppe), while the central and southern regions are semi-desert or desert. However, precipitation rises again in the southeastern mountainous area.
Most of Kazakhstan is covered by plains, or at most by hills at an altitude below 500 metres (1,600 feet). The only mountainous areas are: in the south and south-east (near Kyrgyzstan and China), the Tian Shan, which also includes the highest peak of Kazakhstan, Khan Tengri, 7,010 metres (22,999 feet) high, and in the east (near China and Mongolia), the Altai Mountains. In the mountains, precipitation is more abundant than in the plains, in fact they are often covered by forests, although it depends on slope exposure (for instance the Charyn Canyon, closed among the mountains, is arid). At high altitudes, above 3,500 metres (11,500 ft), there are large glaciers.

Now, let's see in detail some areas and the major cities.
In the west, the area of the Caspian Sea is arid, and in the north coast it's continental, with freezing winters and hot summers: in Atyrau (the former Guryev), the average temperature goes from -6 °C (21 °F) in January, to 27 °C (81 °F) in July, when the days are often torrid. Here are the average temperatures.
Average temperatures - Atyrau
AtyrauJanFebMarAprMayJunJulAugSepOctNovDec
AtyrauJFMAMJJASOND
Min (°C)-9-10-3613182119125-2-7
Max (°C)-3-26172531333225155-1
Min (°F)161427435564706654412819
Max (°F)272843637788919077594130

Precipitation is definitely scarce, about 165 mm (6.5 in) of rain or snow per year. Here is the average precipitation.
Average precipitation - Atyrau
AtyrauJanFebMarAprMayJunJulAugSepOctNovDecYear
AtyrauJFMAMJJASONDY
Prec. (mm)111013131518151311151613163
Prec.(in)0.40.40.50.50.60.70.60.50.40.60.60.56.4
Days87655554467971

On the eastern coast of the Caspian Sea, the climate becomes less cold in winter: the average temperature in January rises to -2 °C (28 °F) in Aktau, and to 0 °C (32 °F) on the border with Turkmenistan, moreover, it becomes even more arid, in fact the annual precipitation is around as low as 150 mm (6 in).
East of the Caspian Sea, the Ustjurt Plateau is desert, with very little precipitation, about 100 mm (4 in), cold in winter (in January, the average temperature is around the freezing point or a few degrees below), and hot in summer, with average highs around 35 °C (95 °F), but with peaks of scorching heat, around 45/47 °C (113/117 °F).
To the east, we find the area of the Aral Sea, a former large lake, once fed by the rivers Amu Darya and Syr Darya, but partly dried up in recent decades, due to the exploitation of the same rivers. Here the climate is desert, with around 150 mm (6 in) of rain or snow per year; winters are freezing, with January averages around -10 °C (14 °F), and summers are hot, with highs around 32/34 °C (90/93 °F) in July. In Aral (formerly Aralsk), which was a port before the lake shrank, the lowest recorded temperature is -38 °C (-36 °F), while the highest is 47 °C (117 °F).
Here are the average temperatures.
Average temperatures - Aral
AralJanFebMarAprMayJunJulAugSepOctNovDec
AralJFMAMJJASOND
Min (°C)-14-14-6512182118113-4-11
Max (°C)-7-54182632343225154-4
Min (°F)7721415464706452372512
Max (°F)192339647990939077593925

Aralsk

About 200 kilometres (120 miles) east of the Aral Sea, we find the Baikonur Cosmodrome, which used to host the Soviet space program and continues to operate under the Russian administration; here the climate is similar to that of Lake Aral, that is, continental and desert.
About 200 kilometres (120 miles) south-east of the cosmodrome, we find the offshoots of the Kzyl Kum desert, which is very hot in summer. In Turkestan, the maximum temperature in July is normally around 36 °C (97 °F).
Average temperatures - Turkestan
TurkestanJanFebMarAprMayJunJulAugSepOctNovDec
TurkestanJFMAMJJASOND
Min (°C)-9-60712171917113-3-7
Max (°C)031221273336332820102
Min (°F)162132455463666352372719
Max (°F)323754708191979182685036

Astana, the capital of Kazakhstan, is located in the north, therefore in the steppe area, which receives a bit of rain more than the centre and the south, because it can experience some thunderstorms in summer; precipitation amounts to 320 mm (12.5 in) per year, with a relative minimum in winter, when it's around 15/20 mm (0.6/0.8 in) per month, and a relative maximum in summer, of 55 mm (2.2 in) in July. Here is the average precipitation.
Average precipitation - Astana
AstanaJanFebMarAprMayJunJulAugSepOctNovDecYear
AstanaJFMAMJJASONDY
Prec. (mm)151515203535553525302020320
Prec.(in)0.60.60.60.81.41.42.21.411.20.80.812.6
Days43358101210775479

Due to its northern location, the temperature in summer is not so high, but it's pleasant: the daily average in July is 20 °C (68 °F). But even here in the north, heat waves in summer are possible, with peaks of 38/40 °C (100/104 °F). Summer, aside from the thunderstorms, which in any case are not very frequent, is sunny. On the other hand, winter is really cold: the average temperature in January, -17 °C (1.5 °F), makes it one of the coldest capitals in the world. In the worst moments, the temperature can plunge to -50 °C (-58 °F). During winter, snowfalls are frequent but not abundant, however, the snow covers the ground for long periods. Spring and autumn are very unstable seasons: in April and October, the temperature can drop below -20 °C (-4 °F), but it can also exceed 25 °C (77 °F). Clashes of air masses can also cause strong winds.
Here are the average temperatures.
Average temperatures - Astana
AstanaJanFebMarAprMayJunJulAugSepOctNovDec
AstanaJFMAMJJASOND
Min (°C)-22-22-16-261113115-2-11-19
Max (°C)-13-11-5920252724199-3-10
Min (°F)-8-832843525552412812-2
Max (°F)91223486877817566482714

Astana

In the far north, Petropavl (formerly Petropavlovsk), has a climate similar to that of Astana, just a bit colder, and a little more rainy in summer: it receives 350 mm (13.8 in) of rain or snow per year.
Even in the eastern cities of Semey (Semipalatinsk) and Oskemen (Ust-Kamenogorsk), the climate does not differ by much from that of of Astana.
Almaty (formerly Alma-Ata), the most populous city and former capital of Kazakhstan, is located in the south-east, in the early slopes of the Tian Shan, and its altitude varies depending on district, however, the centre is at 800 metres (2,600 feet) above sea level. Here the average temperature goes from -6 °C (21 °F) in January to 24 °C (75 °F) in July, often with a large temperature range between night and day; precipitation is more abundant than in other parts of the country, due to its location at the foot of the mountains, and amounts to 585 mm (23 in) per year, with a maximum in spring, between March and May, when intense clashes between air masses occur, which is why spring is also a windy season. In Almaty, there are 55 days with snow per year in spite of the southern location, because of the altitude, which exposes it more easily to cold air masses, so that late snowfalls can occur in spring and early snowfalls in autumn. Here is the average precipitation.
Average precipitation - Almaty
AlmatyJanFebMarAprMayJunJulAugSepOctNovDecYear
AlmatyJFMAMJJASONDY
Prec. (mm)2530659010060352525455035585
Prec.(in)11.22.63.53.92.41.4111.821.423
Days66899874457780

Summer is hot, but the altitude makes the heat more bearable than the plains, and it's sunny as well, although occasionally there can be some thunderstorms in the afternoon, especially in the first part of the season (June-July). During winter there can be cold waves, sometimes prolonged, and in the worst moments the temperature can plunge to -30 °C (-22 °F).
Average temperatures - Almaty
AlmatyJanFebMarAprMayJunJulAugSepOctNovDec
AlmatyJFMAMJJASOND
Min (°C)-11-10-2611151816115-3-9
Max (°C)-1071722273029231660
Min (°F)121428435259646152412716
Max (°F)303245637281868473614332

Almaty

Shymkent is located in the south as well, and at 500 metres (1,600 feet) above sea level, and like Almaty it's located at the foot of the mountains, but more to the south-west, in the South Kazakhstan Province, where intrusions of mild air from southern Asia are possible, in fact in winter this is one of the least cold cities of the country, since the average temperature in January is -2.5 °C (27.5 °F); however, this does not mean that it is not exposed to cold snaps, but only that they alternate with mild periods. Summer is very hot, with a daily average in July of 27 °C (81 °F). Precipitation amounts to 540 mm (21 in) per year, with a peak between November and April: due to the substantial precipitation level, heavy snowfalls are possible in winter.
Here is the average precipitation.
Average precipitation - Shymkent
ShymkentJanFebMarAprMayJunJulAugSepOctNovDecYear
ShymkentJFMAMJJASONDY
Prec. (mm)656080704515838457065540
Prec.(in)2.62.43.12.81.80.60.30.10.31.82.82.621.3
Days109111074212581079

Summer is dry and sunny. This city is windy as well, both for the clashes between air masses, and for the proximity to the mountains. Here are the average temperatures.
Average temperatures - Shymkent
ShymkentJanFebMarAprMayJunJulAugSepOctNovDec
ShymkentJFMAMJJASOND
Min (°C)-7-528131719161151-3
Max (°C)251221273235332719125
Min (°F)192336465563666152413427
Max (°F)364154708190959181665441

In the east of the country, north of Almaty, in the area of Lake Balkhash, a large lake, half freshwater and half saline, located at 340 metres (1,100 feet) above sea level, the climate is strongly continental, with an average temperature in January around -15 °C (5 °F), and in July around 23.5 °C (74.5 °F). In a year, only 140 mm (5.5 in) of rain or snow fall. Here are the average temperatures.
Average temperatures - Balqash
BalqashJanFebMarAprMayJunJulAugSepOctNovDec
BalqashJFMAMJJASOND
Min (°C)-18-17-101915171580-7-16
Max (°C)-11-80132227302821121-7
Min (°F)011434485963594632193
Max (°F)121832557281868270543419

When to go

It's hard to find the best time to visit Kazakhstan, because there is no month which can be safe from either the cold or the heat. In the north and in Astana, in summer, from June to August, the average temperature is pleasantly warm, but you cannot rule out heat waves with peaks around 40 °C (104 °F). In the central and southern areas, the summer heat is more common and often enough becomes torrid, so you may prefer spring and autumn, in particular from mid-April to mid-May, and the second half of September. Around mid-April and mid-September, usually you can find acceptable weather conditions throughout the country.

What to pack

In winter: for Astana and the north, cold weather clothing, synthetic thermal long underwear, fleece, parka, wind jacket, gloves, warm boots. In the southernmost cities, like Shymkent and Aktau, you can wear lighter clothes during mild days, while it's useful to bring a scarf for the wind.

In summer: for Astana and the north, light clothing, T-shirts, but also long pants, light jacket and sweater for the evening and for cooler days; raincoat or umbrella.
For the vast southern plains (Ustjurt Plateau, Turkestan, Shardara), lightweight clothes, loose fitting and made of natural fabric, scarf or desert turban, a sweatshirt for the evening.
For Almaty, Shymkent, the Caspian Sea, Baikonur, the Aral Sea and Lake Balkash, light clothes, sun hat, scarf, a sweatshirt for the evening.
In the southern mountains (Tian Shan), at intermediate altitudes, light clothes for the day, sun hat, sweatshirt and jacket for the evening, hiking shoes; above 3,000 metres (10,000 ft), sweater and warm jacket for the evening; above 4,000 metres (13,000 ft), down jacket, hat, gloves, scarf. In the mountains of the north-east (Altai), the cold starts at lower altitudes: at 1,500 metres (5,000 feet) you already need clothes for spring and autumn, like sweater and jacket.
For women, it is best to avoid shorts and miniskirts, especially outside the big cities.