umm....
You might want to check with your state and local humane laws, friend. What you propose to do could actually be considered cruelty to animals, with some fairly serious consequences for you as well as the cat.
I am a humane officer, and I can tell you that when we get calls for animals trapped in parked vehicles in the sun, we monitor temps and symptoms of heat stress. When cars are in the 105 degree range, typically the animal is coming out of there pronto, courtesy of the law. We have had dogs die because we coudlnt get them out fast enough.
There are a lot of elements to heat stress. You mentioned being able to withstand the heat like that yourself. That's great - but most humans cannot simply walk out into 105 degrees and just be happy or even safe unless they have had the time to adjust their system to that kind of temperature over time. Take roofers, for example. Those guys obviously can tolerate roasting temperatures. If you put most of the rest of us up there for an hour or two on even a 90 degree day, we'd become seriously ill. The reason is that changes happen over time to the thyroid, helping that mammal adjust to it's environment. But we can't do that over a period of three hours. This takes days to weeks. It is also why outside dogs can tolerate being outside in the depths of winter - they build up a tolerance to it and their body regulates itself differently.
Were you planning on wearing a fur coat during your 3 hour sauna at 105 degrees? Because the cat will be. Did you also realize one of the amazing things about humans is that our skin is covered with sweat glands, which help us cool oursleves and help us to
not die of heat stroke, while cats, dogs, etc. do NOT have sweat glands except in their noses and paws. Further, cats don't as readily pant to release heat from their bodies like a dog. When you see a cat panting, things are serioulsy bad for that cat.
I realize this is sounding like I'm really yelling, and honestly, I'm not. I appreciate the inquisitive mind, and I like experiments. It's just that this time, I have to say.....I think there may be a few problems with this one.

I would not do this experiment, unless you do it without any other non-human subjects inside. Of course, you will fry any houseplants you may have as well. BTW, in the days before Frontline, we used boric acid to deal with fleas, and it worked pretty well. This was in CA where they were a year-round scourge.
And in response to your take on the fleas in Arizona...uh....if the heat seems to greatly reduce, but not eliminate all the fleas....you still got fleas, my friend. If you have one, you have a million. Fleas have a few weeks' cycle, so they may seem eradicated for a while, then alla sudden...you start scratching your ankles again

Anyway, by your logic, if the few fleas in the hot states only survive by going toward the shadier, cooler areas.... how will that be any different than in the house? Are you planning on keeping the house 105 forever?? That seems like a pretty dangerous and very expensive flea control method.
Come to think of it, fleas were always less of a problem here in the northern states where they would freeze in the winter. Maybe what you should be trying is freezing your house for a good long while. Same effect - it will kill the adult stages, then you'd have to do it again two weeks later to kill the next wave. Then you'd have to freeze your entire yard. And also, you must never let the cat outside again, in case your neighbor does not adhere to a flea killing protocol, or in case the local mice have fleas. Which they do.
Just sayin'. I think your focus should be more on the life cycle of the flea and less about thermostats, etc., honestly. It might save you some time and money.