Autoformer issue

How long has it been since the plug you had heating problems was disconnected.

If a plug is left for a long time corrosion will build up and cause a high resistance connection.

I have a Hughes Autoformer that was permanently mounted in my trailer. I had used the plug connectors and they were never disconnected as I always used the Autoformer. After about 5 years I discovered the same heating and melting problem you described.

I removed the plugs and made a permanent connection with wire crimps which I soldered after crimping. This required opening the case of the Autoformer which I did not mind as the Autoformer was way out of warranty.

If you do not want to wire direct I would recommend disconnecting and reconnecting the plugs after each trip. This will break the corrosion that forms.

A DC resistance of 10 ohms sounds rather believable. Offhand I would expect a lower resistance, based on a rather simple understanding of how it may be set up, but I don't have any specific values or very detailed design info to be be very certain. The DC resistance of transformer coils is by design quite low since any resistance there simply results in inefficiency and heating. The primary (and also the secondary, or at least a portion of it, since it's the same winding in an autotransformer) would presumably be connected more or less directly to the plug.

Signs of excessive heat at the plug prong is due to a poor connection right in that area, either where the wire attached to it, or between the prong and the spring fingers in the socket it was plugged into, or between the wire and the socket. Replacing the plug is a very good idea if you find it in that condition.

That implies a 12A draw. What is the actual amp draw?