@Charles1938 There’s a lot of unanswered questions here. How long were they there? Did they stay any nights that the her was working? Or did they come in, tell you the heat wasn’t working, and leave right away? Did you have to clean or pay someone to clean after they left? I would refund what they paid minus the hotel but not both full refund and you pay for hotel.
in the future, you and the guest need to work with Airbnb to relocate a guest to another Airbnb, not you pay for a hotel. That’s part of aircover. You could very well be out double now because you didn’t follow this procedure. Not only did you pay for a hotel, but if you don’t issue them a refund, Airbnb could issue them a refund or they could dispute with their credit card and win.