False, this can still happen during their period.
Your body will only be able to function and maintain it's homeostasis at a constant stable temperature of 98 degree's farenheit. It will usually only be able to take a min of 96 or a max of 102. Usually at hitting those max/min, the body will have begun to loose it's ability to mantain that temperature and it could then start beginning a downward spiral of Hypo- and hyper- Thermia, which is very dangerous.
Id say the third option, white blood cells, called lymphocytes, destroy pathogens and protect against future infections.
hope this helps :-)