As a full time RVer who boondocks most of the time, 90 per cent of my discomfort has occurred in summer. That needn't have been so, but it's easy to fall into traps or be timidly conventional.
How drastically I underestimated the southwest in summer! If not for the higher gasoline prices I might have been suckered into going north forever. After all, it really is cooler up north during the shoulder seasons. Would that they lasted longer than two weeks!
The first thing that comes to mind when you say 'four corner states' is the high altitude. Indeed, that is a great help.
But it's easy to underestimate the value of the southwestern monsoon season in July and August. Even before the afternoon sky-and-cloud show, the higher humidity mutes the sun. By noon, the pretty cumulus clouds have formed foamy white tops and darkling bottoms. Soon they flocculate into a thundershower-- transient, local, and topographic.
This praise of clouds and rain must seem surreal to the gooey-ducks of the Pacific Northwest. They love their dry season in July and August, since it's their only chance to expunge the mildew between their toes. But an RV snowbird, who might leave Arizona in mid-April, is already oppressed by cloudless skies.
Besides the mistake of going north in the summer, the other source of thermal misery is solar panels on your RV--literally. This forces you to camp in the hot sun.
Only last year did I transfer my solar panels to the top of my towing vehicle, a van, so that it could bake in the sun, while the travel trailer could sit in the cool shade.
Vans are not common with RVers, but you could do much the same thing with pickup truck/fifth wheel trailer combinations, since most pickups these days have enough of a roof to hold a couple solar panels. But I've never seen any fifth wheelers do this.
A small generator (read, alternator/inverter) made by Honda or Yamaha helps make summer tolerable while you park your trailer or motorhome in shade. Anybody who tells you how noisy and maintenance-intensive a generator is, simply has the wrong one, or is out of date.
Beating the hot sun is a serious profession for RV boondockers in the western states. Either you get serious about it, or you resign yourself to a permanent grimace on your face, eyes that narrow into a squint, finger tips that crack and sting, heels that crack and bleed, facial skin that blotches red into solar (actinic) keratosis, which finally becomes skin cancer.
You walk from the grocery store to your car across a sun-softened asphalt parking lot, feeling worried and guilty about your poor dog in the car which is hot as a pizza oven. You drive out of the parking lot leaving tire ruts in the black, semi-molten goo.

The sun, the aridity, will suck the very spit right out of your mouth. Think of that scene in "The Good, the Bad, and the Ugly," when the Ugly tries to slowly murder the Good by marching him through the desert sun. "They say people with fair skin can't take too much of this sun," the Ugly says. He leers at his victim sadistically, while toying with a dainty, woman's parasol over his own ugly head.
The scriptwriter for this movie blew it. They should have had Eastwood, crawling prostrate in the hot sand, look up with one of his classic squints at the Ugly and his co-murderer, the Sun, and say, "Yea, but it's only a dry heat."