Okay so brainlet here.

My chemistry teacher told me that temperature is just an average. If you take a glass of water at room temperature and measured the temperature of individual water molecules you would see them all over the place.

Generally speaking warm water is less dense than cold water. So warm water will 'float' on cold water. If you left this room temperature water alone long enough would it form a vertical temperature gradient? As in the molecules would eventually vertically arrange themselves based on density which would be dependent on their individual temperature.