Avoid areas with lots of asphalt like Phoenix. Temperature in the cities will peak around 10 PM as the asphalt serves as a heat bank and continues to release heat long after the sun has set. Driving through areas like Phoenix I try to do after midnight. Might hit an armadillo but that is about the only risk and there is less traffic and it will be 20-30 degrees cooler.
Boondock well outside of towns and it will be a lot more pleasant at night. People deal with heat a lot better than dogs so the AC will help your pet keep cool.
From June through August I would avoid spending any more time in places like Phoenix than is needed to get gas and get back on the road.
