It doesn't outright kill individual pathogens, but it does combine the effects of making it harder for them to survive (so letting the population die out) and increased production and activation of immune cells. But that doesn't mean it's a better environment for them than normal body temperature, as of course the system is designed to handle 99% of the infections in that condition. Fever really is the fallback scenario where all bets are off until they fix the issue, causing all the other effects we call 'being sick'.