You've already been pummeled with ideas but here's my thoughts anyway!
IF this had happened to me-- I'd replace the outlet with a normal 20amp
household outlet found at any hardware store or big box home supply.
20 amp outlets have heavier spring pressure on the prongs of any cord
you plug into them.
The outlets found in my RV and most likely yours are wired with cheap
push in wire connections on the back.
This is not nearly as good as stripping a wire and placing it under a screw
which you can securely tighten.
The heat could also have been caused by a defective power cord
on the heater.
The cord end is factory crimped onto the two prongs and then molded
in plastic. If the crimp was defective at the factory, it will get hot as you
It could also have been a weak receptacle as others have already said.
Change the outlet and try again.
By the way, the heat will be generated at the point of MOST resistance
I'm splitting hairs but that's the way it is.
It's normal for the plug to get warm with a heater on high.
It should NOT get uncomfortably hot to the touch.
I also installed a dedicated outlet for my space heater.
My power panel had extra slots for circuit breakers.
They just plug in. They can be found at most any home supply store.
I put an "old work" box in the toe kick area near my power panel and
plugged in a 15 amp breaker and used about 3 feet of #14 romex wire.
It was a simple one beer job but I've been doing this a few years!
Good luck, be careful out there and Happy Camping!!
37 years industrial electrical maintenance
now happily retired 3 and counting