My cable got heated and then the phone display worked but wont charge

There’s a good chance that the phone sustained some extensive damage. However, without knowing if the issue is caused by a bad charger/cable or a logic board issue, it’s hard to say what exactly is at play.

You’ll need to consider that the charge port and/or battery could have been damaged in the process so you’ll need to eliminate those possibilities before looking at potential logic board issues. On the logic board, you could have a damaged Tristar/Tigris IC’s.

Open up the phone and measure the voltage of the battery to see if it is still good. If it measures 0V, you’ll need to get a replacement. Try charging with an original and preferably known-good charger and cable to see how the phone behaves. A USB Ammeter will tell you if current is flowing or not. The next step is to try a known-good (or high quality replacement part) charge port and do the same tests. If the phone still doesn’t work/charge, then it will require a micro-soldering repair.