Another silly option is wear multiple layered suits like it is the early 20th Century again. While all the layers will contribute to overheating and the sweatin

Another silly option is wear multiple layered suits like it is the early 20th Century again. While all the layers will contribute to overheating and the sweating problem, a part of the reason for the layers in the first place (especially in the early 20th Century before modern air conditioning) was to keep sweat to less visible layers. Make sure you stay hydrated, of course. Maybe go Steampunk with it and have fun picking a weird style all your own.