The quick answer is that hot air is less dense than cold air, and less dense materials float on top of higher density materials.

This might be hard to visualize, since we cannot see air, so let’s chose something we can see- balloons. Helium is a gas that is less dense than air at room temperature. So when you fill a balloon with helium, it floats. Now let’s apply this to air: hot air balloons are just filled with regular air from the atmosphere, but they use a flame to heat the air, making it less dense and causing it to float. The same task could be accomplished by filling the balloon with helium (which is actually done in blimps).

The key is always that the less dense gas rises above the more dense gas! When you heat air (or any gas) the energy you are putting into the gas causes the molecules to move faster and spread apart, which by definition means the hot gas becomes less dense (fewer molecules in a given volume).

Thus hotter air = less dense air
so it “floats” on top of colder air.