Imagine for a second that it's the early 100, and you've got an untreatable disease that leads to terrible mental and physical degeneration. Would you let a sketchy doctor trade it for a slightly less awful disease with a slightly better chance of a cure?
That's the logic behind pyrotherapy - a risky technique that was used to treat neurosyphilis in the early 20th century.
Neurosyphilis can happen when you don't treat syphilis - an infection caused by the spiral-shaped bacterium Treponema pallidum. It's rare today, because we can treat syphilis with antibiotics, but penicillin, the first antibiotic, didn't come into widespread use until World War II. Before then, there was no known way to kill the bacteria that cause syphilis. It was a terrible and stigmatized disease, typically spread by sexual contact because of sores that form around the genitals or mouth. The second stage of a syphilis infection involves a fever and a rash. That didn't advance to the dreaded neurosyphilis stage in everyone, but it was a significant risk. Neurosyphilis can occur decades after the initial infection, when the bacterium burrows into the patient's central nervous system and causes a variety of awful symptoms, including dementia-like decline and muscle paralysis.
Even though there was no cure for syphilis, especially the late-stage infection, a Viennese psychiatrist named Julius Wagner-Jauregg noticed that a neurosyphilis patient under his care showed a remarkable improvement after coming down with a fever. He thought that fever might have helped with the disease, but he didn't have a reliable way to cause the fever and test that idea, so he conducted small, dangerous, non-consentual experiments with a protein involved in tuberculosis, typhoid vaccines, and a strain of Streptococcus bacteria - without much success.
Then, in 1917, a soldier with malaria was sent to his psychiatric clinic by mistake - and Wagner-Jauregg seized his chance to carry out another pretty shady experiment. Malaria is awful, too; it's caused by protozoan parasites from the genus Plasmodium, and is transmitted by certain mosquitoes. It causes repeated bouts of high fever, among other symptoms, and is often fatal. But, unlike syphilis, at the time there was a treatment for malaria in the form of quinine - an alkaloid derived from tree bark that's toxic to the malaria protozoa. Quinine had been used by Europeans since the 17th century, and they got it from indigenous peoples from South Africa who had known about it long before then. 
SO, Wagner-Jauregg took blood from the malaria-infected soldier and injected it into some of his neurosyphilis patients - without their consent, of course, which we don't consider safe or ethical medical practice today. They came down with malaria and endured the cycles of high fever until he gave them quinine to stop this. 6 of the 9 patients he treated in this way recovered, at least partially, from their neurosyphilis. When other neurosyphilis patients learned that there could be a cure, they asked to be infected with malaria - and doctors began regularly using the treatment. It's called pyrotherapy, because the goal was to raise the body's temperature, and "pyro" comes from the Greek word for "fire". 
Overall, pyrotherapy cured about half of all the people who underwent it, although an estimated 15% or so died from the malaria instead. And in 1927, despite his unethical experimentation, Wagner-Jauregg won a Nobel prize in medicine for his discovery.
When World War II rolled around, the need for antibiotics was massive, leading to the development and widespread distribution of penicillin. Antibiotics cured syphilis without having to infect people with a dangerous disease that might kill them anyways, so, at that point, pyrotherapy fell out of use. And then another thing happened around World War II, which is that Wagner-Jauregg applied to join the Nazi party. He was a eugenicist and an advocate for racial purity. The fact that the Nazis rejected him is not enough to make him even remotely an OK dude, and the Nobel he was awarded has gone down in history as a regrettable one.
But pyrotherapy did help some people while it was in use, and another unexpected benefit was that having malaria on hand to treat people led to a better understanding of how it grows and spreads. Even though it's malaria that's a global scourge today, without pyrotherapy we could have been a little worse off in our knowledge. Although here's the thing - we're not even entirely sure why pyrotherapy worked; when the treatment was discontinued, so was any study of its effects. Our best guess is that it burns the syphilis bacteria right out of you, because fever is a part of our innate immune system - it heats up to temperatures that are more difficult for infectious agents to tolerate. But, as far as we can tell, the syphilis bacterium is actually fairly heat tolerant, which doesn't support this hypothesis. It could be that the repeated bouts of fever from malaria are simply too much for it, though - we just don't know, and there's not much appetite in the scientific community to find out; you can't really blame them. 
The other strange thing is that if pyrotherapy works because of the heat hypothesis, it shouldn't work on anything besides infections - and neurosyphilis involves mental illness. But, strangely, there are anecdotes going back to the Greek physician Hippocrates that fever could treat a variety of brain-related illnesses like epilepsy. And at least one recent case in medical literature from 2007 shows fever improving symptoms of psychosis. But these cases don't amount to any clear scientific understanding, and if we want to find out whether heat can help ease any mental or physical illness, we need scientific rigor and clear, informed consent of patients - things that weren't on Wagner-Jauregg's radar. 
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