Why does air float when it is hot?

That's not air floating. That is the total reflection of the air near the ground after being heated by the ground. This kind of thing can also happen on asphalt roads in summer. The air temperature near the road surface is higher than the refractive index of the upper air, and the upper and lower layers have different optical refractive indexes, forming a mirror effect. Light emitted from distant objects to the road surface will be totally reflected. Seen from a distance, the road surface is particularly bright and smooth, which can reflect the reflection of nearby objects, just like being drenched by water.