It depends. Do everything you can to keep them from getting chilled... below about 75-80° Do you have any way to heat water? If so, you can put heavy (and I'd double them) Ziplock bags full of very warm water (110° or so.... you don't want to cook the eggs) in the incubator, and keep switching them out as they cool. If you have an old fashioned hot water bottle (for invalids, etc) use that. (if it will fit)

Or rice bags- if you make them out of wool or heavy cotton, you can heat them in a conventional oven (including one heated with wood)

I'd tuck the incubator in the warmest corner you can find, too... if you have a woodstove, stoke it up and put the incubator close to it. Monitor the temps, obviously.

But from what I've read, as long as they don't actually get chilled, an outage of 12 hours or so shouldn't kill them... they may hatch a day or so late, though.

Hopefully, the system will go right by you and it won't be an issue!

Summerthyme