ill nature vs temperament

ill nature and temperament both are nouns.

Word	Noun	Adjective	Verb	Adverb
ill nature	Yes	No	No	No
temperament	Yes	No	No	No

As nouns, temperament is a hypernym of ill nature; that is, temperament is a word with a broader meaning than ill nature:

Other hypernyms of ill nature include disposition.

ill nature (noun)	temperament (noun)
a disagreeable, irritable, or malevolent disposition	an adjustment of the intervals (as in tuning a keyboard instrument) so that the scale can be used to play in different keys
	your usual mood
	excessive emotionalism or irritability and excitability (especially when displayed openly)