Sometimes I would like to pretend I am not Ozz, but this time I am..
The commercially made Propane tank heating blankets might be fine for this, but it really shouldn't be needed unless you are in a really cold place for a long period of time, then you would be getting a large tank, which would solve the problem.
My reason for not liking a heat blanket are many; possible mis-use,(covering up the top of the tank; they don't want you to do that) damage to the heat blanket during normal banging around replacing tanks, improper connection of the power supply; too small extension cord, damage to extension cord... I could go on and on, but I see a few of you nodding off..
I have made my living fixing electrical shorts, burned out elements, bad connections, improper factory assemblies (Think Dimplex fireplaces) I guess I am just a little paranoid, but just would not chance an electric blanket on my Propane fuel supply. I am sure thousands of folks do fine with it.
Yes, it is strange that the one night usage of the furnace and a few other loads can deplete the single battery we all start out with. You would think that the Engineers at design hdqtrs would work that out. At least tell buyers that a second battery may be needed if a person spends a cold night off-grid. I bet most folks find out the hard way.
Don, I think a second one should do it. If you spend a bunch of time off-grid, maybe think of moving up to 4 G.C. even 6 batteries, now would be the time to do it.