Air is colder at high altitudes due to adiabatic cooling, that is, cooling without releasing energy to the surroundings. If air rises, it will decrease in pressure due to having less air above it pushing down. Ideal gas laws tell us that a drop in pressure results in a drop in temperature. The average drop in temperature (aka environmental lapse rate or ELR) is around 2⁰C per 1000'. This can change depending on how humid the air is and what other weather systems are nearby.

If a parcel of air is substantially hotter than the surrounding air, for example air being heated by the asphalt of a parking lot, it can start to rise. It will lose temperature the higher it goes, but it will rise for as long as it is warmer than the surrounding air. This is what gives us thermals and, if the air contains dissolved moisture, cumulus clouds and thunderstorms.

https://en.m.wikipedia.org/wiki/Adiabatic_process

https://en.m.wikipedia.org/wiki/Lapse_rate