That's a rough one. In that heat trying to cool her and the rest of your chickens off is probably a real good idea. You can certainly try to move her to a cooler place but you are correct, she might not accept the move.
A few years back we had a two week stretch with daily temperatures above 110 F. That was miserable, I had a hen die while on the nest laying an egg. She'd been acting sick anyway, maybe because of the heat. The heat does stress them and if they are weakened to start with it can be deadly. That nest was well-shaded and well-ventilated so it should not have been an oven. I don't know what your nests look like or how well they are protected from the sun. A lot if the time a coop is cooler than the outside air, especially a walk-in coop on the ground.
I've had hens incubating eggs with daytime temps sometimes hitting the low 100's. They did OK, those were pretty good hatches. They spent a lot of time standing over their eggs instead of squatting tightly on them. Broody hens are really remarkable about how well they manage incubation. But sometimes conditions can be pretty rough for them.
When I was in something close to your situation I left my broody hens alone and they did OK. My temps were not quite as hot as yours. It's a hard decision, I won't criticize you for whatever you decide.