[AC Question]

I picked up my phone, tried to open an app, and it said it closed all applications because my phone was overheating, but it didn't feel even remotely warm, so I put it down. I came back, and tried to plug my phone in, and it said because of the overheating the battery wouldn't charge. Then it ran out of battery.
Now I'm leaving it plugged in, but every couple seconds the charging indicator pops up as if it stops charging and restarts. I have no idea what's going on, any help?