... just taking the heat related to athletic performance?
Your body being hot from the surrounding temperature is NOT the same as your body and muscles getting heated from athletic activities. They are two COMPLETELY different things.
You should sleep in whatever climate controlled area gives you the best sleep. Energy comes from sleep. Without adequate sleep, you won't perform as well. So... sleeping in a hot, stuffy house is not going to help you what-so-ever.
As far as air purities and stuff... that's a whole different topic. If the air is dry, buy a humidifier. If you live in Los Angeles, buy an air purifier. Haha