When I get a fever (thankfully a very rare occurrence), they seem to flare hotter when I've actually eaten enough calories for my body to burn up. No food, no fever (or greatly reduced).

I learned this fact when I got a bad fever and went to a dumbass doctor -- who prescribed medication which had to be taken on a full stomach -- having a full stomach spiked my fever above 100! (That's "wow, one hundred!" not "factorial(100)".) I had to swear off (at?) food and the medicine.

The bias you're introducing is metabolism. Call yer mum, I'm sure she'll tell you straightaway, "You stop metabolizing right now, young man, or there will be consequences!"