my mobile is getting heat.

So I got my brand new 5S, all nice and stunning. Whenever I use my phone, doing ANYTHING (like using Reeder 2 or just browing offline content in safari reading list my iPhone gets extremely hot. I mean extremely by you almost cannot hold it. I used to have to 4, 4S, 5 and they did not have this problem, I had issues sometimes with them but a clear install(DFU) usually helps and solves everything. I was wondering that it might be the 4G connectivity, but not. As I mentioned, even if I use the phone in airplane mode(mornings) it gets very VERY hot! I think there must be some problems with power amplifying as the normal 5 I had before, got very hot sometimes, but I was able to hold it still and it only got hot if I played graphic intense games.

Apart from that, I claim 2-3 hours of usage battery life with no problem of stand-by time. So if I do not unlock the phone, it gets very cold and nice. But just after I unlock the phone, it starts to boil actually. I think there must be problem with the CPU as it must be running at max clock speed rather than as it should decrease a bit if theres "nothing to do".

I did try turning off GPS, 4G, even 3G. No help at all, even if I use it in airplane mode and only on wifi (nights), it gets hot. I really not sure what to do with it, I dont want to bring it back to my carrier as they would take it and I would get it back in weeks time, as 5S's are very rare these days.

please help me