Caused By Resistance....
Unfortunately, that heat you luckily did recognize, would have been caused by resistance... Either from a severely weakened Cable/ Strand Issue near the Connector or else an actual Breakdown in the Contact Area between the Computer and Cable connectors...
If no visible damage is seen on the cable then should be Warranty I imagine... If horribly melted (did not view pics yet) then hope thety are nice to you!! Mine has always run Cool as can be... Good Luck!!