If it's only a couple 3 hours, I wouldn't even worry about running it.
Here's what I do for almost ever trip:
Pre cool it by running it at home prior to loading.
Freeze a couple half gallon milk jugs full of water to put in the frig when I leave to help keep it cold.
OR
Pre Freeze anything I can to help the frig maintain it's temp. Steaks, Hamburger, metts, hot dogs, etc get frozen at home in the chest freezer then loaded in the frig just before leaving.
If the frig isn't opened and you get it down to the mid-high 30's and follow one of these, you'll be fine for a all day travel trip. I've gone from Chattanooga to Cincy this way in one day with the temp still below 45 when I got home. this was in July with outside temps in the 90's.
Multi day travels, I run on propane but I figure why do it if it's not needed.