Where does 'cooling your heels' come from?

I can't think of a possible scenario where one would tell another to cool his heels (the very first time). Even if you walk a lot, only your legs hurt a lot. Why particularly heels?

How did it come into existence?

Solution 1:

The idea seems to be that your feet become hot with walking and that when you stop walking they, and in particular, your heels, cool down. Hence, the current meaning of having to wait. The earliest recorded use of cooling the feet in this way is dated 1576. Coole their heeles first appears in 1606, where it appears to refer to horses. It is first applied to people in Chapman’s translation of the Iliad published a few years later.