hot up vs heat

hot up is not a noun while heat is a noun.

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

As verbs, hot up and heat are synonyms defined as:

Other synonyms of hot up include heat up.

hot up (noun)	heat (noun)
	utility to warm a building
	the presence of heat
	the trait of being intensely emotional
	the sensation caused by heat energy
	a preliminary race in which the winner advances to a more important race
	a form of energy that is transferred by a difference in temperature
	applies to nonhuman mammals: a state or period of heightened sexual arousal and activity

hot up (verb)	heat (verb)
make more powerful	gain heat or get hot
make more intense	make hot or hotter
gain heat or get hot	arouse or excite feelings and passions
	provide with heat