If heat rises, why is it cold on top of mountains?

You are right that warm air rises. The main place air is heated is at the earth’s surface, where it is warmed by sunlight. So there are always updrafts of rising hot air above us.

As we go up in the atmosphere, air pressure continually becomes less. That means the rising air is expanding. And a characteristic of any gas is that it is cooled by expansion. So the draft of warm air that starts rising from the earth’s surface continually cools itself as it rises. The temperature goes down three or four degrees Fahrenheit for every thousand feet higher we go.