One can get by w/o AC at Bryce. Good elevation (8000') and lots of trees around many of the sites.
For Arches and Canyonlands, it will be pretty hot and with few trees, shade is tough to come by. There are some BLM sites along the Colorado River along UT 128 that get good shade in the morning and/or evening which might work since you'll probably be touring all day. No reservations for those, though and it will still be pretty hot.
At Capitol Reef, the CG is in an old orchard and some sites have shade from those trees. But it's still hot there. You might consider also camping at Singletree NFS CG off UT 12. About 25 miles and 35 minutes to Capitol Reef, but at 8250', much cooler.
The good news is that most nights, the desert cools off nicely. The bad news is it's still blazingly hot in the daytime.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)