Could've fried an egg off my precious
I found my 4s completely powered down and scalding to the touch two nights ago, after little usage - except I did have a few apps (maybe around 10 running in the background - this has never caused a problem before.)
Freaked out, but was able to recharge it the next day - no problem or heating. Decided to delete some photos before backing it up and was browsing when it stopped working after maybe an hour suddenly and it seemed to get hotter once it had stopped.
However, I had not updated to 6.1 - just IOS 6.
When the phone cooled down I started it up, turned off the apps, backed it up and upgraded to 6.2 and it seems to be okay so far...