When is it to hot to cut the grass?

Right now it's too hot!
The best thing I ever did was get rid of the front lawn and install desert landscape. The backyard is still grass but it is not visible from the street. So if I'm lazy or the heat is excessive, I can always blow off mowing for awhile without receiving complaints.
During monsoon season it is humid and hot with lows in the upper eighties. I always mow early before the sun is up beating heat rays at me.
I like the look of a bit of lawn from the backyard deck but mowing is not an activity I look forward to.

Exactly! Right now.

I grew up and live in Eastern South Jersey near the coast. My wife is from the Phoenix area, and her Dad had her cut the grass as a kid. He sat in the shade with a cold one and a stogie "coaching" her on the fine points of yard management. To her it was torture and the heat would wipe her out! I cut my grass whenever it needs it usually after work in the evening. She'll come out of the ac with Chardonnay in hand to pass on some of his indubitable wisdom. "The beer stays colder the faster you drink it!" Hmmm smart guy, problem is my tractor only has one beer holder, and then there's the Green Heads! Damn things are so tough, when you swat them they look up and laugh at you. I love summer in S.Jersey.

It hit 102* yesterday with more of the same expected today. Needless to say the lawn will have to wait.

Most of us in Arizona don't have any grass, it's a waste of water.