Etymology
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Words related to cool

*gel- 

Proto-Indo-European root meaning "cold; to freeze." 

It forms all or part of: chill; cold; congeal; cool; gel; gelatine; gelatinous; gelato; gelid; glace; glacial; glaciate; glaciation; glacier; glaciology; glacis; jell; jelly.

It is the hypothetical source of/evidence for its existence is provided by: Latin gelare "to freeze," gelu "frost," glacies "ice;" Old English cald "cold, cool," German kalt.

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coolant (n.)

"radiator fluid," 1915, from cool (adj.) + -ant.

coolly (adv.)

1570s, "without haste or passion," from cool (adj.) + -ly (2). From 1610s as "without heat;" 1620s as "in an indifferent manner;" 1844 as "with quiet presumption or impudence."

coolness (n.)

Old English colnesse "a moderate degree of cold, somewhat low temperature;" see cool (adj.) + -ness. Figurative sense of "absence of mental confusion or excitement" is from 1650s; that of "absence of warm affection" is from 1670s; that of "quiet, unabashed impudence" is by 1751.

coolth (n.)

1540s, from cool on the model of warmth. It persists, and was used by Pound, Kipling, etc., but it never has shaken its odor of facetiousness and become standard.

keel (v.2)
"to keep cool, make cool," Middle English kelen, from Old English celan "to cool," from Proto-Germanic *koljan "to cool," from the same source as cool (adj.). The form kele (from Old English colian) was used by Shakespeare, but later it was assimilated with the adjective form into the modern verb cool. Cognate with Dutch koelen, Old High German chuolen, German kühlen.
kewl 
1996 as a graphic representation of a casual pronunciation of cool (adj.).
uncool (adj.)
1953, in hipster slang, from un- (1) "not" + slang sense of cool (adj.).
cooler (n.)

1570s, "a vessel in which liquids or other things are set to cool," agent noun from cool (v.). Meaning "portable insulated box to keep things cool" is from 1944. Slang meaning "jail" is attested from 1884. Meaning "long, cold drink," especially a mildly alcoholic one based mainly on fruit juice or a soft drink, is by 1953.

precool (v.)

also pre-cool, "cool prior to use or before some further treatment," 1904, from pre- + cool (v.). Related: Precooled; precooling.