hyperpyrexia vs hyperthermia

hyperpyrexia and hyperthermia both are nouns.

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

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

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

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

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