Phone just died 1 week after screen replacement.

I think you would have to go to the Apple Store and ask them to figure it out, because the phone may have shut off because it detects someone tampering and adding new parts to it. A similar Thing happened to my phone. The screen on my iPhone 5c broke off and when I charged it, the phone got abnormally hot like you said. My 5c also was going erratic after the screen detached (it vibrated randomly and make random sounds without me touching it). So bring it to an Apple Store and lmk how it went.

- thereidfleish