When is it to hot to cut the grass?

Cut your grass at the highest setting and do it after dinner when the sun starts to go down. I cut mine once a week even though it could use it every 4 days or so. I ALWAYS do it on a Thursday or Friday night so the weekend can be kept open for fun things.

Another solution.

Having moved from South Jersey to The Phoenix suburbs a bit less than 2 years ago, I can tell you that it is not fun to cut the grass in the dead of summer in either of those states. That said, the same rules apply. Do it as early in the morning as possible, or when the sun is setting here in AZ. In New Jersey, the mosquitos come out at sunset, so it isn't possible.
I was lucky to get a house that only has what we call a "putting green" of grass in the back, and decorative gravel everywhere else. That is the best way to avoid cutting grass.