That seems over simplistic. Surely there must be some cross-over point between environmental temperature and shower temperature, so you could take a completely neutral shower that won't affect your temperature at all?
Also, I doubt that you could get hypothermia by using close to boiling water in a shower.
There is a cross-over point, it's around your body temp, so usually between 36 and 38C. In France we have thermostatic shower mixer with labeling around this temp, with even a push button lock that can prevent you from going over 38C if you wish.
Isn't this common in the US ?
Also, I doubt that you could get hypothermia by using close to boiling water in a shower.