short temper vs quick temper

short temper and quick temper both are nouns.

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

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

Other synonyms of short temper include irascibility, spleen.

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