caring vs warmth

caring and warmth both are nouns.

Word	Noun	Adjective	Verb	Adverb
caring	Yes	Yes	No	No
warmth	Yes	No	No	No

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

Other hyponyms of caring include warmheartedness.

caring (noun)	warmth (noun)
a loving feeling	a quality proceeding from feelings of affection or love
	the quality of having a moderate degree of heat
	the trait of being intensely emotional
	the sensation caused by heat energy
	a warmhearted feeling

caring (adjective)	warmth (adjective)
feeling and exhibiting concern and empathy for others