We can also confirm that cold eggs can still make it, runner ducks in our experience!
A friend had two duck hens sitting on eggs and they were killed by a predator overnight. The eggs were chilled, but it was summertime and around 60 that night, and she packed them in pine shavings and drove them up to us. The 7 eggs were all at different stages of development, and all 7 eventually hatched into healthy ducklings!
On our next duckling hatch a spring blizzard knocked out power for more than 16 hours. We put a quilt over it at first but when it was clear that the power wasn't coming back on anytime soon, and the incubator temperature was approaching 70 degrees, we took the whole incubator downstairs by the woodstove but could only keep it at about 80 degrees without risking hot spots. We still got a really good hatch rate, especially considering those were shipped eggs.
We also lost power while chickens were hatching during a flood and had the eggs cool while we were dealing with the generator, only a few eggs in that batch but one made it out.
It's such an awful feeling to realize you have cold eggs, but definitely worth plugging it back in and candling a few days later!