In my rural area many Thai men have no issues walking around topless , or they wear their T shirt as a 'belly shower' - great look. I seldom wear a shirt at home, or on my farm - as I will be drenched in sweat within 5 minutes. I always cover up if going to shops or into the city. In the tourist area of my town - it is only the farangs that you see topless - and while they are spending money - the locals tolerate them.
Shirt off while jogging or exercising would be okay - but preferably cover up when you're done.