Cool is a very versatile word. We all know that the word has a lot more uses that those just relating to temperature. Here is a detailed definition that I got from Bartleby;

ADJECTIVE:
Inflected forms: cool·er, cool·est1. Neither warm nor very cold; moderately cold: fresh, cool water; a cool autumn evening. 2. Giving or suggesting relief from heat: a cool breeze; a cool blouse. 3. Marked by calm self-control: a cool negotiator. 4. Marked by indifference, disdain, or dislike; unfriendly or unresponsive: a cool greeting; was cool to the idea of higher taxes. 5. Of, relating to, or characteristic of colors, such as blue and green, that produce the impression of coolness. 6. Slang a. Excellent; first-rate: has a cool sports car; had a cool time at the party. b. Acceptable; satisfactory: It’s cool if you don’t want to talk about it. 7. Slang Entire; full: worth a cool million.

ADVERB:
Informal In a casual manner; nonchalantly: play it cool.

VERB:
Inflected forms: cooled, cool·ing, cools

TRANSITIVE VERB:
1. To make less warm. 2. To make less ardent, intense, or zealous: problems that soon cooled my enthusiasm for the project. 3. Physics To reduce the molecular or kinetic energy of (an object).

INTRANSITIVE VERB:
1. To become less warm: took a dip to cool off. 2. To become calmer: needed time for tempers to cool.

NOUN:
1. A cool place, part, or time: the cool of early morning. 2. The state or quality of being cool. 3. Composure; poise: “Our release marked a victory. The nation had kept its cool” (Moorhead Kennedy).

IDIOMS:
cool it Slang 1. To calm down; relax. 2. To stop doing something. cool (one’s) heels Informal To wait or be kept waiting.

ETYMOLOGY:
Middle English cole, from Old English c l.

OTHER FORMS:
cool ish —ADJECTIVEcool ly —ADVERBcool ness —NOUN

SYNONYMS:
cool, composed, collected, unruffled, nonchalant, imperturbable, detached These adjectives indicate absence of excitement or discomposure in a person, especially in times of stress. Cool usually implies merely a high degree of self-control, but it may also indicate aloofness: “Keep strong, if possible. In any case, keep cool. Have unlimited patience” (B.H. Liddell Hart). “An honest hater is often a better fellow than a cool friend” (John Stuart Blackie). Composed implies serenity arising from self-discipline: The dancer was composed as she prepared for her recital. Collected suggests self-possession: The witness remained collected throughout the questioning. Unruffled emphasizes calm despite circumstances that might elicit agitation: “with contented mind and unruffled spirit” (Anthony Trollope). Nonchalant describes a casual manner that may suggest, sometimes misleadingly, a lack of interest or concern: He reacted to the news in a nonchalant manner. Imperturbable stresses unshakable calmness usually considered as an inherent trait: “A man … /Cool, and quite English, imperturbable” (Byron). Detached implies aloofness resulting either from lack of active concern or from resistance to emotional involvement: He sat through the service with a detached air.

OUR LIVING LANGUAGE:
The usage of cool as a general positive epithet or interjection has been part and parcel of English slang since World War II, and has even been borrowed into other languages, such as French and German. Originally this sense is a development from a Black English usage meaning “excellent, superlative,” first recorded in written English in the early 1930s. Jazz musicians who used the term are responsible for its popularization during the 1940s. As a slang word expressing generally positive sentiment, it has stayed current (and cool) far longer than most such words. One of the main characteristics of slang is the continual renewal of its vocabulary and storehouse of expressions: in order for slang to stay slangy, it has to have a feeling of novelty. Slang expressions meaning the same thing as cool, like bully, capital, hot, groovy, hep, crazy, nervous, far-out, rad, and tubular have for the most part not had the staying power or continued universal appeal of cool. In general there is no intrinsic reason why one word stays alive and others get consigned to the scrapheap of linguistic history; slang terms are like fashion designs, constantly changing and never “in” for long. The jury is still out on how long newer expressions of approval such as def and phat will survive.

MY THOUGHTS
As we can see, the staying power of “cool” in our everyday language has been absolutely phenomenal. I don’t think it is slang anymore. Everyone seems to use this word and it seems to be understood by everyone.