I bring her into bed with me at 5am for the last couple of hours, she has a little feed and goes back to sleep very quickly. But I guess you could set your heater to a timer to just come on for a couple of hours at the coldest part of the night?
My baby wakes anything from 5am to 6am, so I just go with now and get up when she does lol. She did 8hrs last night, so tbh I'm happy with that for now and will just catch up again later