some say the temps should start around 65, some say around 55, but every one agrees on the high end, do not go over 75%, personally i don't go over around 72%, and also don't forget to take into account humidity.
if you don't have an air conditioner up yet, you can put a fan on in the room, but make sure it does not blow onto the chinchilla, keep him out of direct sun light, give him a chin chiller, you can even put it in the frig to make it colder, and also you can put the dust in the frig before he takes a bath. remember also that during playtime, since its hotter, he can over heat easier.
you can tell if they are in distress by their ears, if they are red and you can see the veins, they are too hot, and you need to cool them down very quickly.
i'm not sure if there are other ways to tell, sorry.