Map from Google - Turin

In Turin, capital of Piedmont, the climate is moderately continental, with cold, damp winters and hot, muggy summers. The town is 250 metres above sea level, at the foot of the Alps, along the Po River, in a position that in summer makes it a bit less hot than the rest of the Po valley, and in winter a little less foggy.
Here are the average temperatures of the Caselle airport.
Average temperatures - Turin
Turin J F M A M J J A S O N D
Min (°C) -3 -1 3 6 10 14 17 17 13 7 2 -2
Max (°C) 7 9 13 17 21 25 28 27 23 17 11 8

Precipitation is quite abundant, given that it amounts to nearly 1,000 millimetres per year. The (relatively) driest season is winter, while the wettest periods are late spring, mainly because of afternoon thunderstorms (May is the wettest month), and autumn. Even in summer, however, there's no shortage of thunderstorms.
Here is the average precipitation.
Average precipitation - Turin
Turin J F M A M J J A S O N D Year
Prec. (mm) 50 45 75 115 145 105 70 75 85 105 70 45 980
Days 5 4 6 9 11 9 6 8 6 7 6 4 81

Winter, from December to February, is cold and wet. The sky is often cloudy, and in anticyclonic periods fog may form, although less frequently than in Milan and other areas of the Po Valley. In the middle of the day the sun can come out.
There's no shortage of rainy days, although winter is the relatively driest season.
The wind is generally weak or absent, except when the föhn blows, the warm, dry wind that comes down from the Alps and is able to bring clear skies and good visibility; in these cases the temperature can reach or exceed 15 °C even in winter.
Snow generally falls at least once every year, although it is seldom very abundant (an average of 25 centimetres of snow fall annually). Every now and then, cold air masses from Eastern Europe can bring more or less intense frosts; in February 2012 the temperature dropped to -14 °C.

Spring in Turin is initially an unstable season, in which the first mild days alternate to the return of cold periods, and gradually becomes more enjoyable, especially from mid-April to late May, when there are many nice days, with mild or pleasantly warm temperatures during the day, although in the afternoon or in the evening thunderstorms may break out.
Atlantic depressions that bring rainfall are quite frequent.

Summer, from June to August, is hot and muggy, and generally sunny. Even though wind is generally weak, the heat is bearable more often than in the rest of the Po Valley, due to the temperature a bit lower, but also because of thunderstorms, associated with gusts of wind, which affect the city quite frequently, especially in the afternoon and in the evening. There's still some chance of some Atlantic disturbances, which can bring some pretty cool and rainy days even in summer (but especially in June and late August).

Autumn gives some nice days in September, and sometimes in early October, then quickly becomes gray and rainy. The first cold days usually occur in November.

The amount of sunshine in Turin is not very good from mid-October to February, when the sun comes out quite rarely. The sun however is not lacking in spring, and is frequent in summer, except during the rare rainy days, and the more frequent thunderstorms in the afternoon or in the evening.

Turin, the Mole and the Alps

On the hills that lie to the east of Turin, beyond the Po River, the climate is milder, because in winter they are often above the cold air layer that stagnates in the Po Valley, while in summer they are cooler because of the higher altitude. Here for example, the average temperatures of the Bric della Croce station, 700 metres above sea level, in the municipality of Pecetto Torinese.
Average temperatures - Bric della Croce
Bric d. Croce J F M A M J J A S O N D
Min (°C) 0 1 4 6 10 14 17 17 14 9 4 1
Max (°C) 6 7 11 14 18 22 25 24 20 14 9 6

When to go

The best times to visit Turin are spring and early summer, particularly from mid-April to mid-June. Also September is a good month. However, you should take into account some rainy days in both periods.
Summer can be hot, although less frequently than in the rest of the Po valley, in fact, there may be several acceptable days, especially in June. You have to take into account, in late spring and summer, sudden afternoon or evening thunderstorms.