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Heat in any electrical circuit is caused by excessive current passing through either wires or components in the circuit that were not designed to carry that amount. This could be caused by fault conditions such as a short circuit between circuit paths which causes more current to flow, a component whose nominal value reduces or insulation properties decrease again allowing for more current flow etc.

To determine what is causing the problem you have to either isolate various parts of the circuit in an endeavour to pinpoint the location of the fault and then test components etc to find the actual fault or use a schematic diagram in conjunction with a service manual to locate the fault.

Initially as the heat problem appears to be in the DC-in socket/jack area it would be reasonable to assume that the problem may be located there. As you have already replaced the adapter the next step would be to look at the socket.