I used to work in a restaurant and was almost always in the back kitchen area. In summer, it was so hot the thermometer stopped working because it didn't go above two digits (it was over 115 °F once inside). Somehow I lived with two underworks full binders and my uniform....

And in high school (before I started binding) I wore a hoodie all year round due to dysphoria. I guess I would rather choose discomfort over a panic attack.

If you feel the need to wear a binder like I did, drink lots of water, keep your hair up or short, and find ways to control your breathing so that you don't get overheated as easily (this helped for me, but keep in mind everyone is different).
Otherwise like others have said, sports bras doubled up could potentially work. And what you suggested (a Tri-top) might work too, although I've never worn one for the same reasons as you stated. Good luck.