You also need to tell us which RV ADAPTER you are using. The best one to use is the RV30A-15A LONG DOGBONE type adapter that looks like this.
The small round adapters that look like this all prone to get hot when being used.
If your SHORE POWER 30AMP PLUG now resemble this you will need to replace the cable and plug. You will also most likely have to replace the 15A/20A Receptacle you are using on your house side as well...
You also need to feel your connections when being used heavy and can most likely detect one getting hot long before it does the damage you have indicated.