Hot and Cold water

We filled two test tubes with water - one with cold and one with hot.
We added dye to them both and this is what we noticed:
In the cold water the dye stayed together and gradually dropped to the bottom, as you can see on the right.
In the hot water the dye mixed through quickly and evenly without being stirred.
This was because the particles in the hot water were moving around by themselves, but the cold water didn't move around.