Yellowstone with no hookups?

A small generator is a good idea. we even carry one.

What time of year are you at Yellowstone? How cold do you expect it to be?

As a very, very rough rule of pinkie, one battery equals one night of furnace usage, at least in my mind. Obviously that depends a lot on the battery and the temperature; if the furnace is running more or less constantly it will use a lot more power than if it comes on for a few minutes every half hour or hour.

I would suggest getting the second battery, though it may well be possible to manage decently without it if you don't need too much power and the weather cooperates. You still may need to use the generator to recharge once or twice. If you don't have a multistage converter, that can be a quite slow process.

I also suggest getting something to monitor the battery state that's more accurate than the typical three light indicator panels most RVs come with. A panel mount voltmeter is a very big improvement; a trimetric or similar is even better but also a good bit more expensive.

You definitely can't run a ceramic heater off a battery.

You'll need to use the furnace, like it or not. It takes 1200-1500 Watts to run a ceramic heater. That's a minimum of 100 amps per hour at 12 volts. How many amps in your battery? Remember also you can only really get 50% of the rated deep cycle anls out of a battery.

Based on everything in your post, you should get a Honda EU2000 generator. Yo can run the ceramic heater off that. Plus charge your battery. And it's fairly quiet.

Ceramic heater run off an inverter will deplete the battery very quickly. The only heating option that will potentially last a night would be the propane furnace. As for a generator, all Yellowstone campgrounds restrict generator hours at a minimum, and some do not allow them at all. You will want to be sure you get an inverter style generator because they are much quieter than an open frame contractor style.

We will be there july 3rd. Prob still cold at night. I wil def add the second battery and have been looking around for a Yamaha or Honda generator. The furnace will suffice as heat source. Excited for the trip but a lot to plan for. Three days in Yellowstone and three in grand Tetons. All part of a 21 day trip from RI

Some reading about available amp hours in your battery and the amp hour draw of a even modest electric heater (plus the loss for an inverter) should be your near future. Three days of conservative water use shouldn’t force dumping unless you taking an army. Many of us are dry campers/boondockers. You can have a great time even if not in an RV hotel. Last, I’m a solar guy but a small backup generator comes with me on every trip. Haven’t needed it in the last 6 months but it comes along.

Average lows during the nights are around 40 degrees in early July, according to Google. A heavy blanket or two would go a long ways towards keeping things comfortable (or at least bearable) at night without needing much if any furnace usage.

According to the weather service, the low temps in June should be 38 and July lows should be about 45. You will need some heat but how much you run it will determine your battery life. We set our furnace at 50 degrees overnight and throw on an extra quilt. The furnace only runs a couple of times every night. I recently purchased a Champion 2000i for topping off the battery every day. I should not have to run it very long.
I recently replaced my brand new WFCO converter with a Progressive Dynamics converter because the WFCO would not go into the 14.4 volt rapid charge mode, even when the battery was low to start. After reading about the failure rate of WFCO's, I decided not to bother with the warranty and with what I knew. I had a PD in my last RV and loved it, fast charging and low lost of battery water.

Add the 2nd battery. Get a Mr Buddy portable heater. And you won’t need the generator.
Heater

I was thinking about the buddy heater. How are the fumes with those?