A friend of mine lives off grid in Mexico. His setup is he built a small dedicated brick building adjacent to his parking area and solar array to contain any potential fire, deter any would be thieves, etc. Not quite as thermally stable as a cellar but a lot simpler and cheaper.

Spontaneous battery fires are extremely rare. The cases you hear about are due to damage (a dropped phone or a car crash).

The stove in your cabin (and you) are a far greater risk than a battery would be.

Hundreds of thousands of electric cars have been recalled due to risk of spontaneous battery fires with no damage, recalls initiated due to a dozen or two such spontaneous battery fires occurring in parked, unplugged vehicles. The batteries in almost all cases were manufactured by LG Chem, and the cause of the fires was several potential manufacturing defects, including torn anode tabs and folded separators, that could lead to a short circuit condition when the battery cell expanded and contracted, such as after charging the car. Recalls included the Chevy Bolt, Chevy Bolt EUV, Hyundai Kona EV, Smart ForTwo Electric, Chrysler Pacifica PHEV, and some VW ID.4s. LG Chem's stationary battery packs for home/solar use were also recalled for spontaneous fire risk.

ICE cars are also not immune, for example:

On April 25, 1996, Ford Motor Company announced it would conduct one of the largest recalls for a safety-related defect in the history of the U.S. Department of Transportation. The recall covered approximately 7,900,000 Ford, Lincoln, and Mercury vehicles in the U.S. from model year 1988 through 1993 for a defect in the ignition switch causing the cars to catch ablaze spontaneously (NHTSA recall number 96V-071).

https://www.autosafety.org/ford-ignition-switch-fires/

Although battery fires can easily reach 1500C, and involve reactions that generate oxygen, meaning that depriving the fire of oxygen isn't enough to put it out. The best you can typically do is just let it burn itself out. This works better when your EV is parked outside the home.

My concern would be about what would happen if the battery was sitting beside a house that caught on fire. That seems like a bad situation for firefighters.

Would it be much worse than a car with a full tank of gas in the garage or a few cans of diesel for a generator? A lot more potential energy in those than this battery even if fully charged.

AFAIU, you can stop a gas fire by removing oxygen (e.g. with fire extinguishing foam or a lot of water). Lithium batteries burning reaction provides its own oxygen supply so you can literally do nothing to extinguish the fire. It can burn even underwater.

I think I'd worry about getting rid of heat. You could do that with some pipes or something to couple the heat to the ground over a larger area. I don't think simply burying the batteries would be a good idea but it depends on the maximum heat output and conductivity of the ground.

Batteries used for homes dissipate negligible amounts of heat.

"Underground" would mean a difficult maintenance. The batteries would still need to dissipate the heat which would be extra difficult in a closed compartment. So it will need proper venting, possibly fans.

I think the batteries would need to have a vent and you would want to be able to access them quickly in case of a fire. All I know for sure is that I would not want batteries attached directly to my house.

Although you might get temperature stability, would it be healthy for the batteries? Maybe they work better at 75F than say 50F.

50F should be enough, and will quickly hit ideal temperatures as it heats itself while working.

A stable 75F might be better but I'd rather have stable 50F over unstable 75F.

My car heats its battery below 60F, and it takes about 10 minutes.

A car needs to be ready to discharge at a much higher C than a house battery. So letting the house battery get a bit colder is fine.

Many electric cars have limitations on acceleration when the battery is cold.

Yes, I know.

My whole point is that cars are more demanding than houses.

So the house battery can tolerate a moderately lower temperature while meeting baseline performance.