Check the warranty for your laptop. verify that it is still valid and then consult the warranty documentation that came with the laptop as to what you have to do to make a claim for a warranty repair. (Even if it is out of warranty by a month or so I suggest that you still contact the manufacturer's customer service section anyway regarding a warranty repair)
If it is no longer covered by the manufacturer's warranty read on.
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.
Here is a link to the Hardware Maintenance manual for your laptop.
On p.59 it shows the removal of the systemboard, but importantly it shows that the DC-in jack is a removable module off the systemboard.
If you want to do this yourself you will have to disassemble the laptop as per the manual at least as far as being able to visually inspect it inside, at least initially as far as the DC-in jack area. You will be looking for any obvious signs of overheating etc. it may be that the DC-in jack itself may be faulty and all it needs is to be replaced, but that won't be known until it is inspected and tested.
This may all seem a bit long, but unless there is a known overheating problem with your model laptop and apparently there is but NOT the adapter or the DC-in jack (it is usually the CPU due to blocked air vents) it may have to be repaired by a reputable, professional repair service or the manufacturer.