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Hi therr My iphone 5 which was actually not using from 2012 till now has overheating when in use (even low light and doing normal tasks) And drains battery like a monster . I charge twice a day =max 4 h continus use Aiplane mode with wifi on Im scared to play games cause gets very very hot to touch Ios9.3.2 (same issue with 8.x)
It sounds like you may have a short somewhere. It could be a bad component or maybe a small piece of solder that came loose. You should power the phone off and do not charge it until you have it looked at by a board repair specialist. The battery could catch fire or worse explode. Good luck