frigidity vs coolness

frigidity and coolness both are nouns.

Word	Noun	Adjective	Verb	Adverb
frigidity	Yes	No	No	No
coolness	Yes	No	No	No

As nouns, frigidity and coolness are synonyms defined as:

Other synonyms of frigidity include chilliness, coldness, frigidness, iciness.

As nouns, coolness is a hyponym of frigidity; that is, coolness is a word with a more specific, narrower meaning than frigidity:

Other hyponyms of frigidity include chill, gelidity, iciness, chilliness, nip, frostiness, cool.

frigidity (noun)	coolness (noun)
a lack of affection or enthusiasm	the property of being moderately cold
sexual unresponsiveness (especially of women) and inability to achieve orgasm during intercourse	a lack of affection or enthusiasm
the absence of heat	fearless self-possession in the face of danger
	calm and unruffled self-assurance