heat up vs heighten

heat up and heighten both are verbs.

Word	Noun	Adjective	Verb	Adverb
heat up	No	No	Yes	No
heighten	No	No	Yes	No

As verbs, heighten is a hypernym of heat up; that is, heighten is a word with a broader meaning than heat up:

Other hypernyms of heat up include compound, deepen, intensify.

heat up (verb)	heighten (verb)
make hot or hotter	increase the level of
gain heat or get hot	become more extreme
make more intense	make more extreme; raise in quantity, degree, or intensity
	make more intense, stronger, or more marked
	make (one's senses) more acute
	increase the height of