word-forming element meaning "before," from Old French pre- and Medieval Latin pre-, both from Latin prae (adverb and preposition) "before in time or place," from PIE *peri- (source also of Oscan prai, Umbrian pre, Sanskrit pare "thereupon," Greek parai "at," Gaulish are- "at, before," Lithuanian prie "at," Old Church Slavonic pri "at," Gothic faura, Old English fore "before"), extended form of root *per- (1) "forward," hence "beyond, in front of, before."
The Latin word was active in forming verbs. Also see prae-. Sometimes in Middle English muddled with words in pro- or per-.
Old English colian, "to lose warmth," also figuratively, "to lose ardor;" cognate with Old Saxon kolon, Dutch koelen, Old High German chuolan, German kühlen, all from the root of cool (adj.). Transitive meaning "to cause to lose warmth, reduce the temperature of" is from late 14c. Related: Cooled; cooling.
Figurative meaning "abate the intensity of" is from c. 1300. To cool (one's) heels" wait in attendance, "generally applied to detention at a great man's door" [Century Dictionary] is attested from 1630s; probably the notion is "to rest one's feet after walking."
<a href="https://www.etymonline.com/word/precool">Etymology of precool by etymonline</a>
Harper, D. (n.d.). Etymology of precool. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/precool