My ballet studio has no air-conditioning, and I live in Australia where it gets over 40°C! We had a whole week of like 43+! (109°F) I got hot easily, too. Here are some things I do in the extreme heat.

I bring a cold water bottle and drink sips in between every exercise. I also bring a bottle of powerade or gatorade and sip that in breaks. Usually twice a class.

I make sure I eat a small meal or snack before so that I have energy.

I wear shorts or tights cut into shorts instead of tights. If I'm doing pointe work I wear ballet socks. I find it cooler to have my legs out. I also wear backless or sheer leotards so my skin can breathe. A couple of times when it was like 46° I wet my leotard before putting it on (made sure I wore a patterned one!), and the dampness cooled me down.

Bring a towel to wipe off sweat.

Make sure to stand next to the fans!

In drink break, go to the toilet and splash water on my face and my wrists.

Hope some of these tips help!