The mountain is 14,500 feet high. There is such a thing called the
Lapse Rate which will make it quite comfortable up high even if it is hot down low.
It's on average about 15-20 degrees Celsius cooler on the top of Whitney than in Lone Pine. So if it's 40 C in the valley, which is normal for that time of year, it'll be at best 20C on the summit, but usually cooler. That's below 70F, just to save you from exploding head syndrome with this metric stuff.
In short: July means temps from 100+ in Lone Pine to about 50-55 on the summit in the shade, possibly in the 30s or below at night. And when a storm rolls in, you'll wish you had have brought some extra layers.
