When is it to hot to cut the grass?

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.

Never.

110 degrees in Phoenix is not the same as 90 degrees in Jersey. Leave your grass alone until the temp drops below 85 and drink a lot of water. The humidity level in the Northeast is not something to take lightly.

PLOW it, PAVE it and PAINT it green!

I lived in No NJ for 10 years and my hatred for cutting the grass was legendary, followed closely by my hatred for raking leaves which then had to be bagged and transported to a mulch center. Given that the teenagers in No NJ stopped cutting lawns for pay 35 years ago, HIRE a service and ditch the lawn mower. Money should not be an obstacle, given the type of green you need to pay for a house and taxes in that part of the state. Unless of course, you enjoy trucking ye olde Craftsman to Paramus for Sears to maintain.

Rich