The day is pretty normal, one full sleeve t-shirt will do. The nights are cold. Keep one thick jacket just in case. If you're venturing out at night, better to have a woollen cap and thick jacket, a warm pair of pants since it gets quite windy and that makes it feel even more chilly!
Day will be pretty normal and windy,Nights are really cold, depends on the place where you would stay, if you are planning for camp near chandratal then it is better to have wollen cap and jackets(thermals would be best choice) to keep yourself warm, also recommend you to drink more water to keep your body hydrated.
August mostly gets rains in Northern India but Spiti Valley is a rain shadow region. In general, it remains pretty pleasant mostly but overcast conditions can make you cold in August too. Hence, light woolens are still necessary. Among the list mentioned in this article, the must-have clothing items to carry to Spiti Valley in August are listed as: fleece jacket or light woolen jacket (windproof),
regular cap or hat,
light woolen clothing,
regular socks,
regular sport shoes or hiking boots,
gum boots for bike riders and,
sun glasses
These are the monsoon months when monsoon is in full swing in Kinnaur and it is better to avoid this time as the area is prone to landslides. However, Spiti valley itself remains fine at this time. You can carry light woolen clothes.