Map from Google - South_Sudan

In South Sudan, a country north of the equator and born in 2011 from the division of Sudan, the climate is tropical, hot all year round, with a very hot and dry winter (which may in fact be considered as the summer), and a summer a bit less hot, but humid and rainy.
The country is covered by a plateau, which has an altitude between 400 and 700 metres in the centre-north, while in the south it ranges between 700 and 1,000 metres.
The predominant vegetation is the savannah, more or less arid depending on area, while in the south-west there are also forests, and in some areas crossed by rivers there are wetlands, including Sudd, the largest swamp in the world, situated in the north along the White Nile and its tributaries, which are lost in a myriad of lakes, canals, lagoons, covered with aquatic plants and inhabited by a large number of species of land animals and birds. The summer rains increase the surface area of the flooded areas.

Sudd, a vast marshy area

Other biodiversity-rich areas are the Bandingilo National Park, the Boma National Park and the Southern National Park.
In much of the country, precipitation hovers around 800/1,100 millimetres per year, with a minimum in winter, when it almost never rains, and a maximum in summer, usually in August.
The driest areas are the extreme south-east, on the border with Kenya (where the ilemi triangle, the disputed area with Kenya, is found), and the far north-east, on the border with Sudan; in both areas, below 700 mm of rain per year fall.
Instead, in the far south-west, near the border with Congo, there's a rainier area, in which the rains reach 1,500 mm per year.
Besides some isolated mountains in the far east on the border with Ethiopia, reaching 1,700/2,000 metres, the only mountain range of some importance are the Imatong Mountains, culminating with Mount Kinyeti (3,187 metres) in the south, near the border with Uganda. This is the rainiest area in the country, and is covered with mountain forests. With increasing altitude, the temperature drops, and on the top it's pretty cold all year round.

During winter a wind full of dust can blow in the country, especially in the north. Sometimes during the day it can be very hot, with peaks of 40 degrees, especially at lower altitudes, while in other circumstances it can get cold at night, with peaks of 8/10 degrees.
Between February and April there is an increase in temperature, before the summer rains; during this period the temperature can easily touch 40 degrees, with peaks of 45 °C. In the south, where the rains arrive first, and especially in the south-west, where also the altitude is higher, this spring heating is less pronounced.

The capital Juba is located in the south, at about 500 metres above sea level. Here are the average temperatures.
Average temperatures - Juba
Juba J F M A M J J A S O N D
Min (°C) 19 21 22 23 22 21 21 20 21 21 20 19
Max (°C) 36 37 37 35 33 32 31 31 32 33 34 35

Rainfall in Juba amounts to 960 millimetres per year. Between December and February it almost never rains; it rains more than 100 mm per month from May to October, and the rainiest month is August with 150 mm.
Here is the average precipitation.
Average precipitation - Juba
Juba J F M A M J J A S O N D Year
Prec. (mm) 5 10 40 90 135 120 130 150 120 110 45 5 960
Days 2 3 8 11 13 11 13 13 12 11 8 3 108

As mentioned, in the far south-west the temperatures are more uniform throughout the year, in particular the heat is less intense in the period from February to April, also because the rains arrive earlier.
Here are the average temperatures of Yambio, located at 650 metres above sea level, in the state of Western Equatoria, a short distance from the border with Congo.
Average temperatures - Yambio
Yambio J F M A M J J A S O N D
Min (°C) 16 17 19 19 19 19 18 18 18 18 18 17
Max (°C) 33 34 33 31 31 30 28 28 30 30 31 32

In this area the rains are abundant, around 1,400 mm per year; the rainy season is long, and it exceeds 150 mm per month from April to October.
Here is the average precipitation.
Average precipitation - Yambio
Yambio J F M A M J J A S O N D Year
Prec. (mm) 5 30 85 155 185 175 165 210 190 180 65 15 1455
Days 1 4 8 14 15 16 15 18 17 16 7 2 133

When to go

It's hard to find a best time to visit South Sudan, since a hot winter is followed by a rainy summer. However, given the risk of flooding in large areas in the period of the summer rains, you can choose the winter, and in particular the months of December and January. The weather is nice, but it is very hot during the day, while at night it can sometimes be a little cold. Between February and April the heat increases even more, and becomes definitely torrid, except in the south-west and in the mountains.

What to pack

In winter: light clothes for the day, loose fitting and of natural fabric (cotton or linen), turban for the wind from the desert, a jacket and a sweater for the evening, comfortable boots.

In summer: light clothes, umbrella or light raincoat for the rain showers, light sweater. For the highest areas of the plateau, around a thousand metres, you can add a light jacket.
For women, it is best to avoid shorts and miniskirts.