Can electrical wires be ruined by overheating?
Some newer jumper cables have fuse type elements included, (either a very large value fuse or just a thinner [sacrificial] wire that burns out before the main cable begins to super heat).  This is done to protect those people who have trouble following simple instructions.   Another possibility is that the wire to clamp connection point had a weak spot and that small area burned out during the current overload.

The small increase in resistance (with high temperature) of a thick copper wire is insignificant in this situation.  Even molten copper would pass a lot of current.