Why do things end up at room temperature?
1. There is a certain total amount of kinetic energy in the hot water molecules and an average kinetic energy per molecule that corresponds to a temperature of 80° C. When you add cold water at 10° C, you are adding water molecules whose average kinetic energy is lower. As the water molecules collide, on the average faster ones will slow down and slower ones will speed up until a new average kinetic energy per molecule is reached. The more slow molecules you add, the lower the new average kinetic energy (and thus the lower the final temperature of the mixture).