For a fridge you could freeze the contents in advance if you know power failure is on the way. And fill the empty spaces with frozen bottles of water. Then put the chill to max.
And lay the fridge on it's back so you don't lose all the cold air when you open the door. A good reason to only use chest freezers.
Also insulate the fridge more. Blankets, duvets, The white stuff electonic items come surrounded by has fantastic insulation. Why when I was complaining it was simply too hot to sit on in when we use it on building sites in the summer, did I never think to make my own sleeping mat before we had closed cell ones?
That's a rhetorical queston. Don't answer it!!
qjs