It's a good question but the simplest and best answer is that it doesn't. Hot air only rises when there's cold air and gravity acting on it as well. Here's how it works: in cold air the particles are moving around without much energy. They take up a small volume because they're only tootling from A to B, so a cold gas is a small gas. Heat things up and the particles move around more, which means they spread out and the gas takes up more volume i.e. it expands. This always happens, no matter where you are, hotter gases take up more space.
But now imagine you've got some hot gas in a room and some cold gas surrounding it. Both gases are being pulled down by gravity, so they're both "falling". However, the hot gas is expanding as well, meaning it can fight against gravity a bit. The cold gas, by contrast, isn't expanding, it's just falling under gravity. So the cold gas will drop to the floor. The hot gas will drop as well BUT it's also got kinetic energy that can partially overcome gravity. The effect is that the cold air will, on average, fall better and the hot gas will get squeezed upward. If there's no cold gas surrounding the hot gas, it doesn't rise, it just sits there.
What's more, if you remove the constant effect of gravity, hot air no longer rises, it just expands in all directions. In fact, flames in a space station are perfectly spherical (google "spherical flame in microgravity") So really, hot air doesn't rise. It's actually that cold air falls better.