Great question! To answer quickly: when a molecule has enough energy to float away, it will. Think of it almost like an airplane flying. When the airplane has enough energy (jet fuel), it can escape the gravity of earth and fly away.

In more detail, what you're asking is related to what we call "phases of matter".

There are three main phases of matter: solid, liquid, and gas. When the molecules in a solid gets enough energy, they will turn into a liquid, and when the molecules of a liquid get enough energy, they will turn into a gas. If you're looking for a little more information, like what happens to the temperature of a solid/liquid when it turns into a gas, check out this wikipedia on phase changes.

Warm water is less dense, so gravity does not pull on a given volume of warm water as strongly as it does the same volume of cold water (i.e. the volume of warm water weighs less). It's the same reason why oil floats over water: it's less dense.

The water molecules that are hot wiggle around a lot and push away the molecules near them , so they're not packed so close together. That makes the hot water less dense than the cold water, and they 'float' to the top.

The water molecules that are cold are more sluggish, so they just crowd together a little more. That makes them more dense, so sink to the bottom. I could do an experiment with hot and cold water and maybe food color to test this, but I'll just give you this cool link:

How atoms and molecules are affected by Heat:
atoms and heat