After Misha took off for Sunnybrook, Nila came over to say hello on her way to the baths. According to her, the Flame Sisters have added them to their patrol route, reheating them twice an hour with fire magic.
That sounds like an excellent idea to everyone, and they're split into three large separate areas, so privacy isn't a concern. Cain follows the convoy to the baths, lost in thought and ends up having to stop to get his bearings when he arrives, before finally noticing that they've been labeled. Men, Women, and Open. Since he's the only man usually staying here, he's surprised they bothered to label them, but with Guild Members able to drop by so quickly, the massive baths might be more popular than he thought. It could be just that his schedule is strange, so he never sees them in use.