Do you have it connected to a dock connector at the same time? I know in my experience with an iPhone 4 it does heat up when the screen is On while charging. However, this was in a period of an hour or two. 15 minutes shouldn't cause the phone to overheat like that, even on Skype. I suggest to take it to an apple store like @glenstorey said.
Explain the process you go through with the apple employee. Make two appointments right next to each other so you have time for the phone to warm up to prove there is something wrong. Oh! And do a backup with iTunes on your computer before going to the apple store in case they completely replace the phone free of charge.