Strange iPhone 4 (CDMA) Symptoms

Hi everyone!

I have an old iPhone 4 (CDMA) that was damaged from a charger shorting out (or something of the sort). Supposedly the phone severely overheated when this happened. I got the iPhone from a friend and it had some functionality but needed some serious attention. After replacing the battery and charge port, the iPhone boots fine and runs great. However, after the iPhone has been on for around an hour or so the screen will change and stay at a very dim setting. Changing the brightness in the settings menu does nothing, neither does toggling auto-brightness. Typically within 15-20 minutes after the screen locks to a dim setting the phone will randomly turn off. Using the power and home button together will reboot it back to a usable state. I cannot determine what piece of hardware is failing. My best guess thus far would be the iPhones temperature sensor, I have heard that it will auto-dim the screen in an attempt to lower the iPhones temperature. However in my case the iPhone never gets warm so I believe it could be damaged.

Any input is greatly appreciated guys (and girls)!!