There are many things to do. 1) wrap the tank in blankets, that will help keep the tank warmer. 2) Since I have bio-wheels, if the power goes out, all you have to do is take the wheels out of the filter and float them in the tank. Then, the bacteria do their job. If you don't use bio-wheels, take the mechanical part of your filter and float that in the tank. Lots of bacteria will have colonized there. Although, any mature tank will have all of its surfaces coated in biofilm, a significant portion of which will be the oxidizing/cycling bacteria. Those two tricks will last a poweroutage of a non-overstocked tank for 1-2 days. The fish should not be fed during those days.
If it is going to be more, the battery powered air pump is a good idea. You can take a kettle (heated up on the BBQ grill or an oil heater or kerosene heater or bonfire or whatever) and add some water (not a lot, hot water is less oxygenated) or do a water change with it. In the past I had a UPS (uninterruptible power source) that the filters were connected to, but I gave it to my little brother last year.
My fish survived three days without power after a nasty ice storm last month, just following the things I said in the first paragraph. Fish are more hardy than we usually give them credit for, and both tanks were very mature (several years), so it wasn't really an issue.
I wouldn't blow bubbles through, since your expiration is much higher in CO2 than regular air is. But, swishing the top of the tanks around to circulate the water will definitely increase the oxygen exchange at the air/water interface.
And I don't know where to start with Teelie, since he confused the issues of heat conductivity and heat capacity. Heat conductivity is how quickly heat can move through a medium and would affect how quickly the heat is lost, while heat capacity is how much heat per unit mass an object/media has. Doesn't really have much to do with density, consider liquid mercury 13 times denser than water, but 4 times the conductivity and around 1/40th the heat capacity. Now, liquid water does have 4 times the heat capacity of air, so it takes 4 times the energy to heat up the same mass of water over the same mass of air. But, water does have 30 times the heat conductivity of air. Which means, while air can be heated up, it does not give up its heat nearly as quickly. Consider fibreglass insulation... the fibreglass is good, but it is mostly air, a very good insulator in its own right. This is also why double-paned windows lose much less heat than single paned windows. The biggest consideration here is that there is much, much more mass of water than air in the room, so while the water gives up its heat a little quicker than air will, there is just soooo much more of it, it does take a long time before it loses a lot of heat.