cool (adj.) Look up cool at Dictionary.com
Old English col "not warm" (but usually not as severe as cold), also, of persons, "unperturbed, undemonstrative," from Proto-Germanic *koluz (cognates: Middle Dutch coel, Dutch koel, Old High German kuoli, German kühl "cool," Old Norse kala "be cold"), from PIE root *gel- "cold, to freeze" (see cold (adj.)).

Applied since 1728 to large sums of money to give emphasis to amount. Meaning "calmly audacious" is from 1825. Slang use for "fashionable" is 1933, originally Black English; modern use as a general term of approval is from late 1940s, probably from bop talk and originally in reference to a style of jazz; said to have been popularized in jazz circles by tenor saxophonist Lester Young. Related: Coolly.
cool (n.) Look up cool at Dictionary.com
c.1400, "coldness, coolness," from cool (adj.). Meaning "one's self-control, composure" (the thing you either keep or lose) is from 1966.
cool (v.) Look up cool at Dictionary.com
Old English colian, "to lose warmth," also figuratively, "to lose ardor," from the root of cool (adj.). Meaning "to cause to lose warmth" is from late 14c. Related: Cooled; cooling.