A few quick introductory categories, in case it’s helpful to someone:
Smallest Solution
To the extent that you don’t need to keep the whole house warm, it’s a lot easier to just generate enough heat for your body. Make your heated space smaller, like close off a room, or set up a tent, or just wear warm clothes, or a sleeping bag for sleeping. If you don’t already own or use a winter-rated sleeping bag for cold-weather camping, could be a good backup thing to have in your inventory for this scenario. A zero-degree bag might be overkill for an in-home backup, could likely just go with a a 30-40-50 degree bag. And you’ve always got the option to add blankets on top too… the advantage of the sleeping bag is that it encircles/encloses you, designed to capture and keep your body heat inside. In a pinch, you could probably just wrap up in a bunch of warm blankets and wear some sweatpants/cozy jams, too, for that matter.
To the extent that you want/need to keep up some heat in the house (well above freezing is ideal to avoid risk of busting water pipes), here are some space heating solutions:
Small Heater Solution
Check out something like Mr Heater’s Little Buddy, or Buddy, or Big Buddy size propane heaters, they run on 1 lb propane bottles. I have a Little Buddy and Buddy I use for winter camping, waiting in the front porch for the kids’ bus through winter, etc.
Medium Heater Solution
I have a Mr Heater 75,000–200,000 BTU Convection Heater, made to run on 20 lb propane tanks. I had my furnace go out through the night here in MN mid-winter some years ago (I don’t recall exact temps, but I think it was sub-32F). I ran the heater intermittently in my basement for the evening and again in the morning and was able to keep heat up to basically normal temps while it was running. It’s approximately 2000 sq ft with basement + main level. The open basement made it easy to just run it down there and let the heat spread across the whole ceiling and radiate upward – I also ran some fans to help circulate air. While this one is technically made for outdoor or ‘well-ventilated space’, I only ran it while I was awake and able to monitor. All of these propane heaters burn pretty clean, so I’m usually less concerned about CO (I have CO detectors and keep one nearby propane heaters when heating indoors – I’ve never had one register any amount of CO present). The greater risk, in my experience, is burning low on oxygen levels, especially in a smaller space like a vehicle cabin or tent (you’ll want some cracked windows for fresh air flow). And I don’t use any of them while sleeping.
Large Heater/Furnace Solution*
If you have a natural gas furnace in your house, a power outage does not shut off the gas supply. So if you can power your furnace with battery/generator power, you can run your furnace to heat the house. Some wiring would be needed to allow your furnace to connect to an alternate power source (*not allowed by code, not advisable unless you’re prepared to take full responsibility, etc…).
(*if you do doubt your courage or your strength, read nay further). For power source to plug into, there are battery pack solutions in the neighborhood of car battery size that can buy some hours of run time on an average furnace, I think. A generator is another power source solution, just run an extension cord inside to plug in your furnace plug solution. Even less code-compliant and more dangerous – some folks make plugs to back-feed power from a generator into (one leg of) the house breaker panel via a power outlet (caveat emptor, this is as risky as it sounds if you were to make a mistake in this process. It could cause serious damage to your own property or person, but could also land you in trouble with utilities/authorities if you were to affect something upstream of your breaker panel).
*As a professional, I un-recommend it — as a friend, I’ll just say don’t mess with this stuff if you’re not confident you can handle it. 😉