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I'm sorry to hear about your issue but the phone can't overheat, it will shutdown before it gets too hot, unless you root the phone and overclock it, then it could overheat, or with a custom ROM, both will void the warranty; with that said, your description seems to be a hardware issue, contact your Local support and get it inspected, if you haven't already.
The screen won't crack because of that, could you post pictures of the cracked screen, perhaps someone can find the point of impact
you can post pictures of the back panel, housing, top side bottom.
What did your Local support said about the cracked back?
The phone can't overheat, if the phone was dropped while charging it could damage the port and/or housing and/or any of the panels