Interesting that your original focus was on the appliance. Would suggest after you fix the problem you check out a copy of Electricity Demystified from your local library and then get a copy of one of the rv maintenance guides. You should be thinking 1) from a systems point of view 2) from the source downstream, rather then the load upstream, and 3) as a closed circuit.
When you have a loose connection it reduces the voltage. The appliance is trying to pull the watts it needs so more amps are demanded to make up for the reduced voltage. See watts law. Watts = Amps times Volts.
That is why the wiring and the plug is heating up...the circuit was pulling more amps than it should have. This can happen before the breaker trips or if the breaker is defective....amount of current varies. A good breaker should help prevent you personally from receiving a deadly shock. The circuit breaker system is designed so that when you try to pull too much current through a particular circuit, the breaker shuts off and stops the flow of electricity through it before a potentially hazardous situation develops. In the world of circuit breakers, this is what?s meant by ?tripping?. By doing this, the circuit breaker protects the circuit and its wiring from overheating and causing damage or starting a fire.
Three of the reasons for electrical overheating that leads to electrical fires are excessive current, poor connections, and insulation breakdown. Excessive current is rare, because circuit breakers and fuses (if sized correctly) typically protect against this occurrence.
Poor connections can be very efficient at overheating, because they can generate a high wattage over a small area for a long period of time without tripping the breakers. (again...high wattage) If the watt density is high enough, the connection will glow. An oxide actually forms at the (loose) contact area, and the resistance of the oxide causes the I2R power dissipation. I = amps, R = resistance. A GFCI or AFCI may sense a poor connection after some electrical insulation becomes conductive and leakage current occurs (5 mA or 30 mA, respectively). If a breaker isn't tripping, yet still feels quite warm, you probably are close to having too many appliances on its circuit. Breakers trip because of overloads (too many appliances), or shorts ( bare wires touching each other).
Before you do any work yourself, on electrical circuits, equipment or appliances, always use a test meter to ensure the circuit is, in fact, de-energized.
This would be a good time to go look at your white wires in your electrical cabinets to see if any are turning from white to tan to brown (be sure it isn't dirt you are looking at). You may have more wiring problems now or on the way.