Exercising in SEA possible?

My GF and I are travelling around SEA for 3-4 months starting late October. It’s the first time doing something like this and after doing some research I’ve heard that people often underestimate how hot Thailand is, so it’s crucial to pack the right clothes.

I exercise a fair bit currently, mostly running and the gym. Mainly for the mental benefits but also physical. I tend to sweat more than the average person when exercising so my clothes come straight off and into the wash (although apparently I don’t smell thanks god)

Would it still be possible to exercise 1-2 times a week when travelling? Especially in hot climates like Thailand, where the roads are also hectic.

Ideally I’d take a set of gym clothes, but then it seems like a waste of space as I’m only wearing them to work out. Id also be worried about the clothes just turning a bit grim from all the sweat!

Would love some more experienced travellers advice! Also about how to handle the heat in general