heat (n.)

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.

heat (v.)

Old English hætan "to make hot; 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."

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Definitions of heat from WordNet
heat (n.)
a form of energy that is transferred by a difference in temperature;
Synonyms: heat energy
heat (n.)
the presence of heat;
Synonyms: hotness / high temperature
heat (n.)
the sensation caused by heat energy;
Synonyms: warmth
heat (n.)
the trait of being intensely emotional;
Synonyms: warmth / passion
heat (n.)
applies to nonhuman mammals: a state or period of heightened sexual arousal and activity;
Synonyms: estrus / oestrus / rut
heat (n.)
a preliminary race in which the winner advances to a more important race;
heat (n.)
utility to warm a building;
they have radiant heating
the heating system wasn't working
Synonyms: heating system / heating plant / heating
heat (v.)
make hot or hotter;
the sun heats the oceans
heat the water on the stove
Synonyms: heat up
heat (v.)
provide with heat;
heat the house
heat (v.)
arouse or excite feelings and passions;
Synonyms: inflame / stir up / wake / ignite / fire up
heat (v.)
gain heat or get hot;
The room heated up quickly
Synonyms: hot up / heat up