MAS3:
I never said i know for sure what's wrong.
Well, it's all a bit suspect right now. One would think that if the pin and wire had some high resistance, then it would limit the current, since the whole thing appears to be voltage driven, not constant current source. And if there were no high resistance issue, then why would the connector plastic melt only? The plastic coating of the wire would probably melt as well.
Would be interesting to know what amount of current that a digital pin of an arduino can actually put out (extreme limit) before failing. Not just rated current etc, but maximum possible current.
The OP should try reproduce the issue, but this time put a current measuring device for measuring the current through that ground wire. And have a fire-extinguisher on hand, just in case. And if it is reproducible, then accurately draw the whole system as it is, including manufacturer specifications (connections) diagram of that mains-powered power supply.