Ah ha, that makes sense. Personally, I prefer running everything in a window, so my workaround was a better fit for me than any properly behaving fullscreen mode would have been.
I think some kind of prompt or indicator might be a good idea. If it were my game, I'd probably lean toward having the other character respond to the fire going out and squeeze it in with that dialogue - though maybe that's not a good idea since it's easy to click through dialogue accidentally before having a chance to read it all.
One other thought on the re-lighting UI - since the bar was emptying, that made me feel like my embers were losing heat. Having the bar fill as it gets closer to being re-lit might be more intuitive.