I recently purchased a Knox brand electric cooler (48 watts) than can run on a 12V DC power cable in our PHEV. I haven't used the cooler yet, but I did have a question about using it in the car when it's parked while shopping. I'm assuming I can power the cooler when parked, but my concern is will the PHEV's battery management system be up to the task. If I only had one car battery I wouldn't even think about it, but given the PHEV has a huge battery that feeds the smaller battery shouldn't there be sufficient battery power for short periods of time like an hour or two? I don't want to risk harming either of the PHEV's batteries if powering the cooler when parked is going to do that.
My dashcam will kill the battery on the PHEV if left running without starting the car for approximately 1.5 days. It's happened to me twice now, both times needing a jump-start.
The battery-saver does not do a great job at keeping the crappy 12V battery charged, and kicks off after 10 cycles (or randomly since it never givers me a cycle count).
You can run a 12V connection directly from the fuse panel to power the cooler irrelevant of the on-state of the car, but I wouldn't recommend it for too long.
Undoubtedly your cooler is of the peltier variety, highly inefficient and even less so the higher the ambient temperature. If only shopping for a couple of hours, I wouldn't even bother leaving it on. Just get a cup of ice from McDonald's or somewhere and leave it in with your goods. If you do leave it on, it will not only reject heat from the cooler interior, but add a whole bunch of heat in the process, raising the temperature inside the car.
If you run the cooler and kill the battery, then need to jump the car, you can access a positive terminal under the hood around the front-right under a fuse-panel cover (attach the negative clip to a bare-metal part of the frame/engine and the other end of the cable attach both clips directly to the good battery).
The PHEV really needs a beefier 12V battery IMHO, and if I was keeping mine I'd definitely stuff the biggest one I could in there, or maybe even a LiFePO4 battery, since the usable SOC is so much greater without causing damage to the cells.