Arizonians don't typically stay in parks in the summer. They head for cooler temps.
You might consider taking I-40 across to Amarillo, TX & then dropping down to I-10. Along I-40 in AZ, it will be a lot cooler than I-10. Flagstaff is one of the places southern Arizonians go to cool off. You have to think elevation to get cool - above 6,000'; preferably 7-8,000' EL.
If you're only planning on one night as you travel it's very doable in AZ. The nights cool way down.
Regardless, if you want I-10 in AZ with multiple night stays it's doable with the AC running a lot.