Hot water stays on the top of cold water and doesn't mix. This is because of difference in DENSITY of water at different temperatures.
When we heat water, then the atoms gain energy from the heat and start moving away from each other. Now, when the atoms move away from each other than the (mass per unit volume) i.e. the density decreases. This makes water lighter.
When the temperature is less i.e. cold water then the atoms are more compactly packed and therefore the density of water is more at lower temperatures.
Since, hot water is lighter than cold water that is why it stays on top of the cold water.