That's not much to go on. Did anything happen before this started (software update, dropped, has it ever got wet)? And when you say both "white and black" and "won't turn on", do you mean that it temporarily went black and white and now won't turn on at all, or that it still lights up in black and white but the phone won't boot properly any more? And if you shut it down (pull out the battery for a couple of minutes if it is removable) and try to restart it, does the screen remain completely black, or do you e.g. get the splash screen image and then it goes black when it tries to load the OS? Information like this would help pin down the problem.
Basically though, if the splash screen lights up, or if you get a normal display when entering the bootloader, but it goes black if you try to boot normally, then that would suggest a software problem of some sort (because the screen would be working when you weren't running Android but going black when you were, which would mean the hardware was OK and the problem was in the OS somewhere). If it won't light up at all under any circumstances, it's most likely hardware.
The screen heating sounds like hardware to me, but I'd like to be sure. If it's a software problem you might be able to fix it with a factory reset (if user software or settings) or reflashing the phone (if system software - less likely). If it's hardware there is nothing you can do except get it repaired or replaced.