I never sweat and get overheated to the point of passing out..what are some things I can do?

I have Hypothyroidism and one of the symptoms is reduced sweat, or 'hypo'hydrosis. I was recently diagnosed and put on a low dose of Levothyroxine and I haven't gotten a second blood test yet to see if I need a larger dose or not (which may help me sweat more). In the mean time, what are some ways to keep my body cool or ways to keep from fainting/passing out? The heat my body generates is so intense now that I can barely sleep at night. It feels like I can't breathe well and everything is stuffy :(