For how long could I power a portable fridge with the traction battery when car is off?

That’s a 200 volt inverter? That’s cool there expensive. Where did you get yours?

 

I'll vote: let go of that notion; have the car fully on.

 

That’s an expensive inverter.

And you better have a newer battery because putting an aux load on a 2007 battery will not end well especially if your in the boonies. You would have to closely keep an eye on the B+ and make sure you don’t go below the go/no go on the battery level. I have seen a few discussions on what the minimu battery voltage must be to spool the engine. Like 205 volts????

 

You would be breaking new ground for sure, given that in all the history I've seen of people attaching high-input-voltage inverters to the traction battery, it's been de rigeur to attach it at the system main relays, where it will be safely unpowered whenever the car is not in READY mode.

Toyota put a lot of effort into building that system so that whenever the car's off, or the main relay gets deactivated in a collision, there's no high voltage to surprise anyone. You would be adding a strong element of surprise (and perhaps liability, should the person getting surprised be a first responder, say).

Getting to the quantitative question, when Dometic gives an Ah-per-hour rating, I believe they are assuming a nominal 12 volt input, so you're looking at 12 to 24 watts. (I'll just say "watts" here, rather than the somewhat redundant "watthours per hour". We understand this is an average figure for once the fridge is down to the set temperature and cycling, and it really draws more watts than that when running.)

The traction battery when new is built from 6.5 amp-hour modules, strung together for 201.6 nominal volts, a total capacity of about 1310 watthours. The car takes care to use no more than 40% of that capacity (usually that between 40% and 80% actual state of charge) and under normal circumstances will try to keep the state of charge right at 60%.

If you power the car off under normal circumstances (battery near 60%), you'll have 20% of that capacity available above the preferred low limit of 40%. 20% of 1310 is 262 watthours, giving you 11 to 22 hours of run.

If you like to live on the edge, you could probably double that, and use 40% of the battery capacity, which starting at 60% would take you down around 20%, which reportedly is about where the car says "nope, not starting this engine" and becomes a large paperweight, until you find someone with a 200 volt charger who makes house calls. So those would be 22 to 44 hours of run.

All those figures are for a battery with the spanking-new capacity of 6.5 Ah. An older battery could be down to half of that capacity or less; realistically, cut all the numbers above to half or a third, unless this is a spanking new battery you've just put in.

The 12 volt battery that comes in the car is 540 watthours, comparable to what you actually get to use out of the traction battery, and larger 12 volt batteries of easily double that capacity are widely available (if you don't mind them not fitting in the battery well). So for this application, it might not be that the fuss of attaching to the traction battery even buys you much.

Another possibility to consider is if the fridge is averaging 12 to 24 watts, an 80 watt solar panel feeding your 12 volt battery might replace a 24-hour day's usage in a good 8 hours of sun. Prices on panels in that ballpark don't seem too bad, judging by a quick Google search.

Running off the 12 volt system also means you're not adding the inefficiency of yet another inverter (besides the one that's built into the fridge, which is included in their efficiency specs) into the picture. If you're looking at a high-input-voltage "plug out" inverter, that's probably a pretty big unit. My experience with both the old ConVerdant 3kVA and the AIMS 2kW units is that they'll use around 25 constant watts just for their own entertainment, comparable to the upper number in the range given for the fridge itself, so cutting your run time in half or worse.