This is my setup
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It's not the prettiest thing but it works. I've taken this setup to many camping trips so far, sleeping in the car. We don't carry a tent. Our Tesla uses Li battery.
It uses a small 222wh rechargeable battery rated at 100w you see in this picture, pulling power from that "12v" socket from Tesla. Then it provides more reliable "12v" pure sign wave power to the fridge. This particular fridge pulls around 50w-ish normally and goes up to 80w-ish at the startup. Battery never heats up, just mildly warm to the touch.
When you are not using the car, this battery will keep the fridge going for 4 hours or so. When you are driving, or in "camp mode", obviously it will fill up and also power the fridge. The battery default to DC output (although, 110v is available), so if it completely drains itself, it will power back the fridge nicely if you use DC.
Not the prettiest thing I have ever created, but it vents and doesn't overheat. Vents of this fridge are all on the front and right side of the unit. Doesn't produce much heat even when set to coldest freezer setting. Ice creams harden up just fine, over time.
We plan to take this setup (along with other camping gear, including Exped Mega mat) for 3-week long trip east, and a month+ long trip this winter down south.