I run my fridge on AC through my inverter while driving.  The 12V circuit
is just "on," no thermostatic control, but the AC circuit has thermostat so
it doesn't freeze my food on the long winter drives.  If I'm stopping for
an hour or less I'll just leave it on that system.  The inverter shuts off
if the DC voltage gets down to 10.5 or something so it won't kill my
battery if I forget it.

Edward