For those talking about hyperthermia killing, yes but in almost all those cases the cause is not an infection.
In fact, I would say that paracetamol kills a hell of a lot more patients than it actually ‘saves’.
A study I have taken to heart is that permissive hyperthermia (up to 40 deg c) in ICU patients has a greater survival than those where fever is treated aggressively.
Physiologically, this resonates because high temperatures activate the immune system and raised temperatures are non-optimal for bacterial proliferation; so the immune system is primed by fever; suppressing it can dull immune system response.
In fact, malaria was used as a treatment for syphillis in the early parts of the 20th century because high temperatures kill spirochetes. There are also a decent number of case reports of cancers going into remission following fever.
However in my quick mobile google then I could only see the following study that demonstrated no advantage for either control of permissive hyperthermia group in ICU patients; so perhaps I was relying on a study that has been superceeded.
You don't want to stop a fever ~ just keep it within the safe zone where it's healing, but not dangerous.
In fact, i cannot think of any disease that literally kills. Even with the big stuff like cancer or aids, it is always the symptoms that get you. They damage body systems and the decline of those systems (aka symptoms) eventually causes the cardiac arrest or internal bleeds that shut off nutrients to the brain. Those symptoms are just as lethal no matter thier cause. A massive fever that stops normal body chemistry, whether caused by flu or ebola, will kill you just the same.