I'm faced with the same problem. Replacing the battery on used one didn't solve it. I tried to freeze my phone in fridge, eventually I succeed and it turns on, I install program to check battery temperature and found an interesting moment. Temperature began rising from 10 till 25 evenly in 2 or 3 minutes and then it began immediately jumping ~25 to ~65 and back. After few minutes when it reached 70+ phone turns off. Maybe this information will be useful. Have any ideas?