Once you're into the Rockies, NFS campgrounds in the higher elevations will be plenty cool without AC. We often camp in the Bighorns at around 8K feet with our 5th wheel, and we always use some heat at night, right through July and August. Without it you'll need warm sleeping bags, and be sure to have some warm clothing -- at least sweater/sweatshirt/wool shirt and a light jacket, and of course bring rain gear.
On weekends you might have trouble finding a camping site in a FS campground, but during the week if you stop by 3-4 p.m. you should be fine. Dispersed camping in the national forests is free, but you won't get a toilet, picnic table or drinking water.