It's a little dirty back there!
I've only noticed it on the kitchen faucet, but I haven't specifically tried on the others. The kitchen faucet has individual hot and cold valves.
There is nothing else near here that would heat that cold water line. The hot water heater is located just to the left (from looking under the kitchen sink) of where the cold water comes into the camper.
I'm guessing, as others have suggested, that the check valve running to the hot water cold inlet is bad. Does anyone know if it would be the white or black part shown in the pictures?