cool has 15 distinct synonyms spread across 6 of its 12 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its 2 recorded opposites are warm, heat.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
neither warm nor very cold; giving relief from heat
“a cool autumn day”
marked by calm self-control (especially in trying circumstances); unemotional
“play it cool”
inducing the impression of coolness; used especially of greens and blues and violets when referring to color
“cool greens and blues and violets”
psychologically cool and unenthusiastic; unfriendly or unresponsive or showing dislike
“relations were cool and polite”
the quality of being at a refreshingly low temperature
“the cool of early morning”
2 of the 12 recorded senses carry no synonym, antonym or related term, so they are not shown above. Every sense, with its definition and examples, is on the full entry for cool.
Synonyms, antonyms and the broader and narrower relations for cool come from Princeton University’s WordNet. Full sources and licences.