Putting dry ice in the coolers should do it. Stuff's so cold that if you don't separate food container from dry ice with newspapers or cardboard, the food container gets frozen.
A gasoline- or propane-powered auxiliary power unit (i.e. generator) would be a much better power source for that than the truck's diesel engine.
Would a typical cheap gasoline generator (small and likely unoptimized engine) be better than a modern diesel car engine?
Probably not. Cheap gas generators use a ton of fuel.
I dunno if that is really accurate. A diesel engine is really just a generator.
Electric perhaps, but I'm not sure about a gas generator -- two-stroke engines tend to be very polluting.