Hey man,
I've been dealing with the same issue lately. It's been hot because of the summertime but I find that even when most other people are feeling comfortable inside, I am still sweating.
My advice is to find a thin undershirt (fruit of the loom, hanes, etc.) and wear it as a normal shirt. No one is able to tell that it is really an undershirt and they're super cheap and will help keep you a little cooler than a thicker t-shirt. They usually come in a few different colors (black, grey, white, brown, etc) so as long as you don't mind dressing a little plainly, you should be good to go.
Best,
Escher