Watchman campground in the park is an excellent place to stay. It has electric and water and dump facilities. There are plenty of trees for shade. It's an easy walk to the visitor center and catching the shuttle bus. Anywhere around Zion is going to be hot.
However, Bryce National Park will have very pleasant weather because it's much higher in elevation. The campgrounds inside the park don't have electric but there is shade and again, it's not that hot. Right outside the national park is Ruby's which is a full-service facility with camping, restaurants, laundry, fuel. They have full hookups.