Galaxy s 3 overheating seemingly out of nowhere
I had an S4 for a while and now have a Galaxy Note 4. My family has the S5 and S6, I believe, and all of them have gotten very hot while charging at one point or another, but not with an error. 

Check to see if your charger reads 5V - 2A, which is what should be on the S3. You could try charging while the phone is off - just watch its temperature.