Mike, excessive heat build-up in the shore cord can be caused by any number of conditions. The cleanliness of the contacts, the amount of current flow, how tight the connection, etc., are but a few of them. You mention you replaced the “plug” twice so I’m assuming you didn’t replace the entire shore cord. To remain code compliant, it is mandatory to replace the entire cord if the plug cap becomes damaged, burned or distorted. Replacement plug caps are available, true, but we don’t recommend using them since the wires connect to the plug with a screw/clamp type of attachment, typically. Amperage flow, a higher or lower than normal voltage source and loose, dirty, corroded contacts will eventually cause those screw/clamp type attaching points to weaken over time. By code, the plug should be contained inside a molded plug cap that is sealed around the cord. This provides a safer, more secure, less moisture-prone connection. You'll want to avoid an overheated condition like the plug above was subjected to!
But I always recommend you measure the voltage and check the polarity of the voltage of the park pedestal before plugging in and to make sure the prongs on the shore cord are clean, dry and tight. Here’s a little video I produced that explains my recommended cleaning procedure.
Also, if you are drawing close to maximum current flow while plugged in, that would add to the heat factor too. But check to make sure the plug contacts are clean and engage as a snug fit into the receptacle. You can carefully (ever-so-slightly), reposition the hot and neutral prongs on the plug to tighten up the fit in some cases. The receptacle itself may have been worn from years of service in that campground also. Any arcing during the transfer of energy will weaken the contacts and cause overheating.
Also, consider ordering my eBook about the 120-volt AC system. It details the individual tests you can perform before plugging into any AC source of electricity. You can order it here.