A note about processors in mobile devices, they don't throttle until the service is loaded, so heat doesn't necessarily imply anything. If it's not getting the point of the throttling control, it's not going to idle down.
It's really difficult to tell what is going on with them and unless you can get a point of adb - which if that isn't loading it won't log.
JTAG is the most sure fire way to fix it. That being said if it's something you want to try on your own, it's quite at your own risk, there are some difficulties involved. Part of the trouble is the partition scheme can quite vary from different models, so if they did something that messed up the partitions themselves it's a bit difficult to recover from.
If the wrong boot/recovery/system partition was flashed then it would still likely be able to go to download mode, the fact that it doesn't is not a great sign.
The stock boot partition would probably be around 5 or 6 mb.
Stock ROM is available here:
http://www.sammobile.com/firmwares/download/7396/I957DUXLI2_I957DTLSLI2_TLS/I'm afraid I'm not too much more help here.