coolness vs frigidity

coolness and frigidity both are nouns.

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

As nouns, frigidity is a hypernym of coolness; that is, frigidity is a word with a broader meaning than coolness:

Other hypernyms of coolness include cold, coldness, frigidness, low temperature.

As nouns, coolness and frigidity are synonyms defined as:

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

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