i live in a desert type of climate. You get use to it like people have to get use to the cold weather. 120 f inside a gym? No big deal just make sure you are in shape.
i still think it will help burn fat quicker because when the bodies core temperature rises the body burns more fat. I think it is the same when you run in a sauna suit. your training output may not be as high in such hot heat but your body temp will definitely rise, you will lose mainly water weight but may also lose some fat if you have some to lose. If you are already in shape and have low body fat %, then i see no benefits
do your running in the morning or dusk so youre not out in the sun. drink lots of water if there is no AC in your gym atleast get a fan, put them by the little windows so you can get some air moving, it will help alot. my old man put in an exhaust fan in the ceiling of the garage and it helps tremendously