We did the same but in reverse Denver to Moab to Yellowstone back to Denver. Rental car in Denver, they don't tell you about the Toll road fee and hail damage insurance on the rental rate from Denver Airport when you book the car. We put 2,000 miles on the car in 10days and rented a jeep for 2days. Some jeep rentals will pick you up at the Moab airport.
We went in July and it was HOT (Dry heat) but not totally unbearable. Second day we used the rental car floor mats in the jeep made it a bit cooler in the jeep.