When we dry camp, we very rarely run the furnace. When we get up in the morning (usually me first), I start the percolator coffee maker on the stove top and about 1/2 hour later the coffee is done and the camper is heated up. Then when everyone is up, making breakfast usually requires us to open the windows to cool down the camper! (of course, keep in mind making sure the camper is ventilated with vents and/or windows cracked open)
Sleep with warm quilts and/or sleeping bags for comfort.
Or... have a quiet Honda or similar generator, and run it during the day to recharge the batteries.
You may very well find that with careful use, your battery power will be fine for a weekend.