Just throwing it out there, but the locations of maximum heat generation are where the resistance is highest. But the TOTAL AMOUNT of heat generated is greatest when the total resistance is low, which means lots of current.
So a large amount of heat will be generated in a circuit which has low resistance, and will be focussed at the point in the circuit of highest resistance.
The power brick should have quite low resistance (to increase efficiency), and the insides of the computer should have a high resistance, limiting the amount of current.
Does the power cord still charge your computer as quickly as it should?
I would say it's either a chip of metal in the connector, or a damaged cord. Either one could be causing a partial short, causing the current flow to be greatly increased (hence much more heat) or an increase in resistance, causing the heat generation to be focussed at the connector.
I expect finding out what's wrong would require a multimeter.
But the end result is simple. Get it replaced.