As other's have said, you will need to go with GC2 6v batteries in series to get the amount of capacity you a looking for. Being in Alaska I know what your talking about when it gets cold at night. What we typically do is turn on the generator about 30 minutes before calling it a night and then crank the furnace up to 70, then when I kill the generator I would turn the heat down to 55-60.
Reason for doing so was to try and get a full charge on the batteries prior to going to sleep, while also getting it nice and toasty. In the morning I would do the same thing. I would go outside and fire up the Yamaha until it was warm and my wife had gotten up etc, then I would kill the heat during the days. Because of people going in and out, water pump etc I would run the generator about 30 minutes - hour at lunch time till it was fully charged.
Either way, look into some 6 volt batteries and then go from there.