You have a crimped terminal that's overheating. Those are not good for high current motor connectors. Either the crimp was bad, or the ring terminal wasn't tight enough on your connector. You'll have to cut off all the burned wire and replace it as it will still overheat, now that the individual copper strands are burned. You should probably get better connectors for all three motor wires, which are the heavy blue, yellow, and green wires.
All of this is simple, but needs some good technical repair skills.
Whether that solves your controller shorting issues, I don't know, but it's clear that the previous owner under designed the motor connections.