my iphone 5 (32gb) is also overheating. i'm pretty certain it's not a software thing as i did a full restore and back up 2 days ago and it's not helped at all (although it did help with the other issue i had). i'm not a gamer (unless you count scrabble and card games which are hardly full on in terms of usage) so i'm pretty sure it's not that. i'm using the net a lot as i don't have a proper internet connection at home yet, so lots of browsing, facebook and such. i do have location switched on so i'll see if turning it off helps, but the most heat seems to be generated if i make calls - i get to feeling my ear is on a fryer.
edit: that said, it does cool off very quickly too. i made a call just before making this post and it was really hot, and now i've written the post it's stone cold again.
the battery doesn't seem to be draining too fast but then my previous phones (galaxy s2, iphone 4 before that) drained even faster so i don't have much to base this on.
maybe if it's an apple thing there could be an update with a fix? if it's a hardware thing - i bought my phone thru verizon, should i go to them or to apple? in the past (and for all my other apple hardware) i've had apple care and gone to apple but not this time. would apple still be able to help?
edit 2: i'll try restoring from new rather than backup as per previous post, see if that helps at all...