Why is it called a "heat?"

I was explaining how to read a heat sheet to someone. English is his second language. He asked, "Why is it called a "heat?" I didn't have an answer, other than that's the term that is also used in track and field. But it got me wondering, why is it called a "heat?" It doesn't really make sense when you think of the more common definition of the word, which has to do with temperature. One online dictionary has 20 different definitions for the noun "heat." One of the definitions is: Sports. a. a single course in or division of a race or other contest. b. a race or other contest in which competitors attempt to qualify for entry in the final race or contest. Then I searched an etymology dictionary, and found this: Meaning "a single course in a race," especially a horse race, is from 1660s, perhaps from earlier figurative sense of "violent action; a single intense effort" (late 14c.), or meaning "run given to a horse to prepare for a race" (1570s). This later expanded to "division of a race or contest when there are too many contestants to run at once," the winners of each heat then competing in a final race.