What do you have for batteries before you get to worrying about inverters?
Generator on board?
Out side temps is going to be the big factor. I have unplugged mine several times at night (Batteries going bad) but was looking at overnight temps into the low 50° to mid 40°. Temp rise was within the safe limits. Remember that without opening the door during the day the compressor won't be running much even if you have power.
If it were me I would try it a few times. Maybe a couple gallon jugs of ice to help it cool.