Might it be more mustachian to find your hot water pipe, pipe it in through the wall, snaking back and forth a few times, and create a towel warmer through the convection of your hot water? It'd be quite simple and inexpensive. I wouldn't expect it to make your towel steamy hot, but certainly warmed nicely while you shower. However, if you take mustache type 3min showers it may not work. Just my 2c.