Another suggestion.
You could put the heater in your garage (or somewhere else where the temperature is similar to the RV) and let it run for awhile (like overnight), then feel the plug. If it feels about the same as when in the RV, then "likely" all is well. If it is a lot cooler, then I would consider replacing the outlet in the RV.
I also choose to run a heater (set very low) in my winterized trailer, and the plug is not warm at all. But then I don't try to keep the temp above freezing, just warmer than outside.
Steve