iPod touch 4th gen overheating

My theory is something got damage when it originally got smashed and the screen replacement has triggered the malfunction

I would say you are right, I had similar experiences with hot chips and it has to do with shock damage. An iPod touch I had the same problem and it also had a flickering LCD backlight (it would go out randomly and the come back on every 30 mins or so)

I ended up taking it apart and took a heatgun to the chip hoping it might reflow the solder a bit. Welp I ended up frying the chip in the process.

If I was you I would just be thankful that its working half decent and put up with it. If you go and try to fix it, be prepared for a total loss.

It happened to my ipod to try to keep the light below half to save energy and if you jailbroke your ipod try to keep background themes off thats all I got if that doesnt work take your ipod back and get a new one.