IMHO only... won't be the input voltage per se.
I would suggest that Compressor would be lucky to have a 20 minute on 40 minute off duty cycle so it would def get get super hot at 20 minute continuous.
The leads being copper (which obviously conducts heat) are probably the source of the heat that melted plug which is quite close to the compressor IE the leads will get bloody hot and melt the plug
To test that theory... run it for about 10 mins under load and check how hot the leads get.
If the leads get bloody hot then that is the issue, if they don't then it was most likely a poor connection at the plug.
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