quick temper vs short temper

quick temper and short temper both are nouns.

Word	Noun	Adjective	Verb	Adverb
quick temper	Yes	No	No	No
short temper	Yes	No	No	No

As nouns, quick temper and short temper are synonyms defined as:

Other synonyms of quick temper include irascibility, spleen.

quick temper (noun)	short temper (noun)
a feeling of resentful anger	a feeling of resentful anger