Can heat effect my unborn baby?

I’m 6 months pregnant. I was suppose to close on the house We bought last week but something came up and didn’t close on the house we bought because of paperwork and we gave our apartment notice we’d be out, so we’re staying at my moms, and I live in florida and she doesn’t believe in putting the ac on. She thinks if it’s on 78° and not on, it’s on. It’s central air. I tried telling her its only on when you hear it. The house is about 80° at night when I sleep and I put a fan on and I wake up dying. Really hot and sick and a migraine. I have to go outside and breathe. Can this effect my unborn baby??? I really don’t have a choice right now and I’m super worried... I also feel my baby move less there some reason. Advice 😢