If you've already factory reset it I don't think recovery will help you: the main thing you can do with a stock recovery is reset the phone, it doesn't do a lot more. Indeed how did you wipe the cache if you couldn't get into recovery?
So what are you actually trying to do? Not "get into recovery", but what do you hope that being in recovery mode will let you do?
Second question: do you know your password to get past the FPR lock? Because I would deal with that before doing anything else. If you are lucky the reset will have fixed the problem and this is all you need to do now. If not you can find the software to reflash it at Sammobile.com (possibly via ATT as well - some US carriers provide this for some of their phones).
Just to warn you though, rebooting and getting hot might not be a software problem, those could indicate a hardware fault instead. So there is no guarantee that any of these software interventions will fix it - we can only hope.