Cracked screen and overheating?

Hi there, basically what it is, I cracked my iphone's screen and back casing about 2/3 months ago, which hasn't bothered me much at all as it still works and does everything as normal. Updated to IOS6 the other week also and it's a bit slower. But earlier today about midday I had a warning message pop up about my phone overheating, thought nothing of it, swiped the screen and didnt touch it for half an hour. It's been on charge for the past 2 hours and I went to check it and it's not turning on. Does anyone know any way of resolving this or had similar problems? I don't think the screen or casing has taken part in the problem as it's been in this condition for 2/3 months.

Can I take the phone to apple and even pay for a replacement if the phone isn't repairable? Thanks, Steven.