Then I would stop in Cruces. Get a good night's sleep and start out as early as you can, get through as much as AZ as you can before the heat of the day. Have lots of water with you.
There is a portion of I-8 after the California border where you drive thru a mountain pass with a steep grade. The signs say "No air conditioner for the next 10 miles to avoid engine over-heating." Turn off the air, open the windows and get a drink from your cooler. Never had a problem there, just wanted to warn you. And after the pass the temperature starts to drop. My favorite part of the drive. Watching the car thermometer drop from 110 to 72.