Galaxy s 3 overheating seemingly out of nowhere

[Amyautopsy]

Phone is fairly new to me, I got it November or so. It's always worked just fine. Today I had it plugged in, walked into the other room for a few minutes and came back. Phone showed an error something like "Charging paused. system is too hot." So my Boyfriend told me to restart it and put in my extra battery (because I have two batteries for it). Did that, powered back up, was working on where in settings I could find the battery temperature and (less than 5 minutes)it told me something to the effect of "System overheating. all apps have been closed, phone can only be used for contacts". So I powered off, pulled out the battery, and now I'm nervous to try and turn it on again. Any suggestions?

EDIT: I'm not rooted

 

[srkmagnus]

Leave it off for a bit to cool down. Power back on and let us know how that works.

If it's a temperature problem it should restart and be back to normal.

 

[Amyautopsy]

Leave it off for a bit to cool down. Power back on and let us know how that works.

If it's a temperature problem it should restart and be back to normal.

It's been off since I posted. Put battery back in and just powered up. Battery is now at 1%. Phone stayed on without error until it died, but still seems to be getting warm quickly. the heat doesn't appear to be from the battery, It's like it's getting hot behind the power button on the side. Or the space between the battery and that button.
Should I try to put a charger in it and see what happens?

 

[Amyautopsy]

It's been brought to my attention on another forum that this phone should be charging with a cord that says 5V-2A. The one I was given with this phone says 5V-0.7A. Is that maybe what fried it? I've located a USB to wall plug that reads 5V-2A, but I'm not sure how to choose the "right" Usb cord to use with it (I have many). Any advice?

 

[Amyautopsy]

NEVERMIND. I tried to put in a charge cord and it showed me one of those yellow warning triangles and a thermometer.

 

[Amyautopsy]

It starts flashing the triangle/thermometer as soon as I plug it in (even though it's not hot) and then starts getting hot after disconnected from the charger now. I can't power up to check anything else because the overheat killed both my batteries.

 

[B. Diddy]

Welcome to Android Central! Does your Settings>Battery menu show any app that's using an inordinately high percentage of battery?

Also, if you have an SD card inserted, Unmount it (in Settings>Storage), then remove it and reboot. A corrupt card can sometimes cause significant overheating.