hyperpyrexia vs hyperthermy

hyperpyrexia and hyperthermy both are nouns.

Word	Noun	Adjective	Verb	Adverb
hyperpyrexia	Yes	No	No	No
hyperthermy	Yes	No	No	No

As nouns, hyperthermy is a hypernym of hyperpyrexia; that is, hyperthermy is a word with a broader meaning than hyperpyrexia:

hyperpyrexia: extremely high fever (especially in children)
hyperthermy: abnormally high body temperature; sometimes induced (as in treating some forms of cancer)

Other hypernyms of hyperpyrexia include hyperthermia, febricity, febrility, fever, feverishness, pyrexia.

hyperpyrexia (noun)	hyperthermy (noun)
extremely high fever (especially in children)	abnormally high body temperature; sometimes induced (as in treating some forms of cancer)