Old English hætu, hæto "heat, warmth, quality of being hot; fervor, ardor," from Proto-Germanic *haita- "heat" (source also of Old Saxon hittia, Old Norse hiti, Old Frisian hete, German hitze "heat," Gothic heito "fever"), from the same source as 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 the meaning "run given to a horse to prepare for a race" (1570s). The latter word over time was extended 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, especially of females, corresponding to rut in males. 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-stroke is from 1858. Heat-seeking (adj.) of missiles, etc., is by 1955. Red heat, white heat are in reference to the color of heated metals, especially iron.

"unsubstantiated statements, boastful talk," 1900, from hot (adj.) + air (n.1). The adjectival phrase hot-air (of balloons, etc.) is from 1813.

also hotdog, "sausage on a split roll," c. 1890, American English, from hot (adj.) + dog (n.). Many early references are in college student publications; later popularized, but probably not coined, by cartoonist T.A. "Tad" Dorgan (1877-1929). It is said in early explanations to echo a suspicion (occasionally justified) that sausages contained dog meat.

Meaning "someone particularly skilled or excellent" (with overtones of showing off) is from 1896. Connection between the two senses, if any, is unclear. Hot dog! as an exclamation of approval was in use by 1906.

hot-dog, n. 1. One very proficient in certain things. 2. A hot sausage. 3. A hard student. 4. A conceited person. ["College Words and Phrases," in Dialect Notes, 1900]

Related: Hot-dogger; hot-dogging.

"short-shorts," 1970, from hot (adj.) + pants (n.). Probably influenced by earlier sense of "sexual arousal" (1927).

also hotspot, 1888 as a skin irritation; 1931 as "nightclub;" 1938 in the firefighting sense; 1941 as "place of international conflict." See hot (adj.) + spot (n.).

c. 1400, literal; 1530s in figurative sense of "trouble." See hot (adj.) + water (n.1). Hot-water bottle is from 1895.

also hot-bed, 1620s, "bed of earth heated by fermenting manure for growing early plants," from hot (adj.) + bed (n.). Generalized sense of "place that fosters rapid growth" is from 1768.

"passionate," 1590s; a relic of old medicine and medieval physiology theory; see hot (adj.) + blood (n.).

"hastily," c. 1300, from hot + foot (n.). As a verb in U.S. slang, from 1896. As the name of a prank played with matches, by 1934.

"short-tempered person," 1650s, from hot in the figurative sense + head (n.); Johnson's dictionary also lists hotmouthed "headstrong, ungovernable;" Elizabethan English had hot-brain "hothead" (c. 1600); and Old English had hatheort "anger, rage," literally "hot heart."