Lots of cheapo jumper cables have 10 or 12awg copper clad aluminum wire, with really thick wire insulation to make them appear as if they are real jumper cables.
These questions are for my curiosity.
How much trailer battery do you have?
Can you see the melted jumper cable wire thickness at the alligator clamp? guess at the wire gauge? Where did the insulation melt?
Your tow vehicle's alternator might overheat with thicker jumper cables attached to those depleted batteries. Do you have a way of measuring its temperature? 220F is the max 'safe' limit, and can be acheived in about 10 to 15 minutes, perhaps less, when maxing out an alternator without moving the vehicle. It really depends on vehicle platform.
Underhood airflow and higher alternator rpms when driving spin cooler air through the alternator, faster, making driving more effective than idling, and easier on alternator. Higher Idling rpms will move alternator fan faster, but perhaps not move underhood air any faster.