I bought two iphone 5s 32 silvers today. I set up both of them, one for my boss. I noticed when I picked it up that it was super warm compared to mine. I will see if it continues. I am sure he will let me know.
Was his restoring from a backup at the time, I know my 5 got warm during the restore after updating to ios 7.
Mine did the same and there was lots to restore. Cool as a cucumber now and the battery is doing great considering I can't keep my hands off of it!