The main climbing season is May to September. May is cold: June is the most popular month: July and August warmer and more unsettled: September cold again. Denali is sometimes called the coldest mountain on earth, and in winter it is a place for the fanatical few. In the main climbing season the temperatures above are the normal minimums you would expect to encounter (possibly a few degrees colder in May and September). But there are important points to remember about conditions on Denali:
The windchill effect can be severe.
Storms can last for days even in the summer.
Because of its high latitude there is less oxygen high on Denali than on a similar Himalayan peak. 6000m on Denali will feel like 6600m in the Himalayas.
Wind chill rating: Severe
The approach to base camp is either long (10 day) trek or a short flight - either way light and compressible gear is an obvious advantage.
Climbers usually move up through a series of camps to a high camp at about 5200m: with supplies of food & fuel needing to be carried up for these camps, the lighter the gear the better.