In addition to the answers regarding pathogenic loading, the circadian rhythm of the body plays a role in both temperature regulation and, it's suspected, may interact with the pathogen: https://doi.org/10.3389/fcimb.2019.00425

I'd also add that, for the malarias, they tend to fall into cycles of synchronisation in their reproduction with points where they're more exposed to the immune system (free in the blood) coinciding with the most severe portion of the fever (made worse by the preceding hemolysis).