If the trip isn't long and the door is opened enroute, it should stay cold enough inside. However, most residential fridge installs include an inverter, powered by a sufficient battery bank to keep it running as needed for the duration of the trip. Or longer. The engine alternator supplies enough amps to keep the battery charge up while driving.
Most fridges can get along fine on 1000w-1200w of inverter power. They actually use only about 200-250W while running, but the compressor start cycle or an ice maker cycle can briefly bump the load up to 700-900 watts.
As donn, Dan and Gary say, it's running off of an inverter all the time. There's wa-a-ay more battery than needed for that, and the coach generator makes up for a lot of the drain (there's more than just the fridge running off of that inverter) while driving, even for rest/fuel stops, so plugging in or running the generator after setting up for the night replenishes things quickly.
When I installed our residential fridge I also installed a dedicated 600/1200 watt pure sine-wave inverter. The momentary max draw on startup for our fridge is ~720 watts and ~200 watts running. For the past 4 years this setup has been trouble free.
I installed a residential in our 5th wheel a while back and run it off of a pure sine wave 2000 watt inverter while traveling. I have a wire hooked up from the truck to keep the batteries charged on the 5th wheel while we are on the road. So far it has worked great. The inverter has a transfer switch built into it so it runs off of city power when we are plugged in or when unplugged it automatically switches over to battery. The inverter you will want to mount as close to the batteries as possible and run the 120 lines as needed. On ours I found the breaker that ran the fridge, which also runs the tv, then removed that line and ran it to the inverter. Ran a new line from the breaker to the inverter transfer switch. One of the reasons I switched was our RV fridge quit and after reading of all the fires caused by these fridges, we decided to do the switch. I'm glad we did because when I removed the RV fridge there was some darken wood from the heat that was just starting to char.
Most fridges are good for 8 hours or more without power... Beyond that they get a bit too warm (This assumes you do not open the door) I max at about six hours on the road then I park.. your millage (or hours) may vary. That said. I went with an absorption unit.. In my trailer days I had a small "Office/Dorm" size and then i did some longer drives with it. Never had a problem as it was locked in the trailer while i drove.