Hot air rises, but mountaintops are always much cooler. Why?

Dear Tom,

Hot air rises, so a mountaintop should be warmer than the surrounding valleys, but this isn’t the case. Mountaintops are always much cooler. Why?
— Tim Lindner, Ankeny, Iowa
Dear Tim,
It’s certainly true that “hot air rises,” but it’s not as simple as that. Hot air at the same air pressure as cool air rises, but air pressure decreases as one goes upward. Air pressure at 18,500 feet above sea level is half the sea level pressure. Air expands as it rises due to pressure decrease, and expansion causes a decrease in temperature: 5.4 degrees for every 1,000 feet of elevation increase in dry air. Dry air with a temperature of 100 degrees at sea level will have a temperature of 0 degrees at 18,500 feet. Saturated air decreases less, at about 3 degrees per 1,000 feet of elevation increase.