I know this is an aside, but speaking as a physician the treatment of fever doesn't actually do much of anything [1]. The rates of certain injuries e.g. febrile seizures are the same with or without Tylenol [2].
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1488736/, https://www.ncbi.nlm.nih.gov/pubmed/12076499/ [2] http://adc.bmj.com/content/88/7/641