Technically heat doesn't really rise. What we call heat is essentially molecular motion. The more molecular motion, the greater the heat. Heat moves from high motion to low motion (hot to cold).
In the lowest part of our atmosphere (the Troposphere) temperature (on average) decreases as you go higher, primarily because it gets farther away from the Earth, which is a primary heat source. The further from the source of energy you get the colder it will be, just like a cool night around a campfire. As long as the campfire puts out the same energy, the temperature profile as you move away from it will be fairly stable. The same is true for our atmosphere. Our global energy balance is relatively stable and the temperature profile through the Troposphere is also relatively stable and gets cooler the further form the Earth. Hence, mountains are cool.
Above the Troposphere, is the Stratosphere, and it does the opposite. It gets warmer the further you move from the Earth. This is due to the Ozone layer absorbing solar energy. Some of this heat actually goes downward into the cooler parts of the atmosphere.