I am on a HP ProBook 4530S now, and like the above post said, it's not at all normal for the charger connector to get that hot.
Could be that the charger is overvolting your computer, which might in turn cause the computer to burn (pure speculation, but likely).
Click on start, type "HP power assistant" in the search box and see if you have this installed. if not, check the HP support website and see if the HP power assistant application is available for your laptop model. This software gives you warnings if it detects issues with the power supply/ internal battery, and would be a good starting point to begin troubleshooting. Are you sure it's the connector itself heating up, and not the computer heating up and inducing the heat to the connector?
EDIT: just read that link on how you fixed the charger. it's not a very good idea to do it yourself, unless you are really comfortable doing it. and I wouldn't recommend people to try this at home at all. A better (stable/long-term) solution would be to purchase a new DC cable, and replace the whole thing from the brick, you can do this at home too, you will need a soldering iron though, but it's what i would have done in case my charger broke and i didn't want to trouble HP support.
Are you sure the charger is working now? Does the battery icon in windows system tray say "plugged-in, charging"?
Do you have a multimeter to check the terminal potential difference while the charger is on, and resistance between the terminals when the charger is off? If you do, then please post these readings (P.Diff in Volts, R in Ohms). If resistance is zero, then there still remains a short circuit.