i wonder if there are studies about hot bath. Onsen are extremely popular in japan, and i'm absolutely certain the relaxation you get from hot water is beneficial to health as well
I'm sure I read somewhere that cold showers can be dangerous for people with per-existing heart conditions too.
I can't cite either right now but they should be easy to find with a Google search.
I think cold showers trigger the diving reflex[0] ("most noticeable effects are on the cardiovascular system, which displays ... in humans, heart rhythm irregularities"). I don't have a real source for that, but I tried cold showers a few times and found it impossible to breathe when I had cold water spraying on my face, like I could feel my airway closing involuntarily. Warm/hot water doesn't do that.