heat (n.) Look up heat at Dictionary.com
Old English hætu, hæto "heat, warmth; fervor ardor," from Proto-Germanic *haita- "heat" (cognates: Old Saxon hittia, Old Norse hiti, Old Frisian hete, German hitze "heat," Gothic heito "fever"), from PIE *kaid-, from root *kai- "heat." The same root is the source of Old English hat "hot" and hæða "hot weather" (see hot).

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. Meaning "sexual excitement in animals" is from 1768. Meaning "trouble with the police" attested by 1920. Heat wave "period of excessive hot weather" first attested 1890; earlier in reference to solar cycles.
heat (v.) Look up heat at Dictionary.com
Old English hætan "to heat; to become hot," from Proto-Germanic *haita- (see heat (n.)). Related: Heated (with many variants in Middle English); heating. Compare Middle Dutch heeten, Dutch heten, German heizen "to heat."