low temperature vs cool

low temperature and cool both are nouns.

Word	Noun	Adjective	Verb	Adverb
low temperature	Yes	No	No	No
cool	Yes	Yes	Yes	No

As nouns, cool is a hyponym of low temperature; that is, cool is a word with a more specific, narrower meaning than low temperature:

Other hyponyms of low temperature include chill, gelidity, iciness, chilliness, coolness, nip, frostiness.

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

low temperature (adjective)	cool (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