I bet it takes one bathful of water to heat it up before you dare refill and get in. On a motoryacht I did some work for, the owner had a solid cast bronze bath in his bathroom. We seriously considered fitting it with electric heating for the same reason. I've no idea what they actually did in the end.
When we were discussing engine heaters for the winter, I remembered this morning that I used to have a little flat oil heater which I left under the sump in the cold winters. It had a safety wire gauze over the flame to prevent oil vapours catching light.