I did a 4-corners camping tour by car a few years ago during July. It was a very hot, dry summer but we lucked out and had relatively cool weather because a cold front had just passed through. We camped at Arches, Mesa Verde, Grand Canyon and Zion national parks, and we also drove through parts of Canyonlands, Monument Valley, Bryce Canyon, Escalante and Capital Reef. We did a lot of hiking at every park we camped at, with distances ranging from 4-5 miles to 10+ miles. I could have easily cycle toured in the weather we had that week, but I don't think it was typical. However, in general the humidity is very low there, so the heat is not oppressive like you get in the Southeast.

Perhaps the biggest problem you might encounter is the long distances between towns, campgrounds and places to get food and water. That problem would be exacerbated if the weather was really hot. Regardless, the scenery is incredible -- even outside the national parks. I thoroughly enjoyed driving in that area.