Why does my Iphone 4S get warm and eat battery?

So I got my new phone a few days ago and can't help but notice that it gets pretty warm after about 20 minutes of using facebook and the app store. I'm also losing 1% battery every 3-4 minutes while using it. Is this normal? I have tried turning off 'locations' on most apps and left it on for weather etc. Removed my icloud account but it still gets quite warm. Concerned it will damage the phone, thanks for any input!

You have some app that is running
and it is drawing data (also) and because it is running, it is eating battery power.

Press and hold the main button.
a list of running apps should come up at the bottom - you can select ones you don't want/ should not be there and kill them.

iCloud is not the problem
It is a good thing - leave it there
It does backups automatically while you are charging AND you have Wi-Fi available and enabled.