Etymology
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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.

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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. Bartlett ("Dictionary of Americanisms," 1848) reports that het, as past tense and past participle of heat, is "Often heard in the mouths of illiterate people." Compare Middle Dutch heeten, Dutch heten, German heizen "to heat."

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up (n.)
"that which is up," 1530s, from up (adv.). Phrase on the up-(and-up) "honest, straightforward" first attested 1863, American English.
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up (adv.)

Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."

As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.

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up- 
prefix with various senses, from Old English up (adv.), corresponding to similar prefixes in other Germanic languages.
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up (v.)

1550s, "to drive and catch (swans)," from up (adv.). Intransitive meaning "get up, rise to one's feet" (as in up and leave) is recorded from 1640s. Sense of "to move upward" is recorded from 1737. Meaning "increase" (as in up the price of oil) is attested from 1915. Compare Old English verb uppian "to rise up, swell." Related: Upped; upping. Upping block, used for mounting or dismounting horses, carriages, etc., is attested from 1796 (earlier was horsing-block, 1660s).

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up (adj.)
c. 1300, "dwelling inland or upland," from up (adv.). Meaning "going up" is from 1784. From 1815 as "excited, exhilarated, happy," hence "enthusiastic, optimistic." Up-and-coming "promising" is from 1848. Musical up-tempo (adj.) is recorded from 1948.
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cover-up (n.)

also coverup, "means or act of concealing" some event or activity, 1922, from the verbal phrase (1872), from cover (v.) + up (adv.).

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pop-up (n.)
from 1906 as a type of baseball hit; from pop (v.) + up (adv.). As an adjective from 1934 (of a children's book, later toasters, etc.).
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up-country (n.)
"interior regions," 1680s, from up- + country (n.). As an adjective from 1810; as an adverb from 1864.
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