Should you avoid cooling a frying pan with water?
If you cool a pan too quickly it could deform, especially if your using a cheap pan. A cast iron pan could crack. This is most likely to happen if you dip a hot pan in cold water.

If you want to get a jump-start on cleaning, de-glaze the pan with a cup of water as you would when making gravy. Pour off this liquid and set the pan aside to cool completely.