cool vs cool down

cool is a noun but cool down is not a noun.

Word	Noun	Adjective	Verb	Adverb
cool	Yes	Yes	Yes	No
cool down	No	No	Yes	No

As verbs, cool and cool down are synonyms defined as:

Other synonyms of cool include chill.

As verbs, cool and cool down are synonyms defined as:

Other synonyms of cool include chill.

As verbs, cool and cool down are synonyms defined as:

Other synonyms of cool include cool off.

cool (noun)	cool down (noun)
the quality of being at a refreshingly low temperature
great coolness and composure under strain

cool (adjective)	cool down (adjective)
neither warm nor very cold; giving relief from heat
psychologically cool and unenthusiastic; unfriendly or unresponsive or showing dislike
inducing the impression of coolness; used especially of greens and blues and violets when referring to color
marked by calm self-control (especially in trying circumstances); unemotional
fashionable and attractive at the time; often skilled or socially adept
being satisfactory or in satisfactory condition
used of a quantity or amount (especially of money) for emphasis