Battery powered air pumps are a must in cases like this. I have one in my tank and one in the filter box as well. When the power goes out they automatically come on.
As far as using a computer back up power pack...not worth the money for the few minutes that it's going to work (IMO).
You can remove the filter media and place it inside the tank itself. Especially if you use a
HOB or canister filter. By doing this and having the Battery back up air supply your good bacteria will still get oxygen that it needs to survive.
As for keeping it warm. I suggest a generator. It's the only way to go. Wrap the tank in blankets will help some.