Every once in a while, I will be defining a common medical or biological term which sounds like it was devised by Martians. It wasn’t. The Greeks are usually to blame.
The word comes to the English language via modern Latin, itself having scooped up the word purexis from the Greek. The root pur- means fire. It is the same root that is used in the words “pyrotechnic” and “pyromaniac”. A patient with a fever is said to be “pyretic”.