People have noticed that the iPhone does get warm with extended video watching. Warm is okay. Too hot to touch would be a problem, and could be related to your initial problem, in which case, a replacement might be in order.
See:
http://www.apple.com/batteries/iphone.html for more information on extending battery life. In particular, it is worth noting that you should close any apps properly by pressing on the home button for several seconds until the home screen appears, rather than navigating away from the app, which may leave some processes running in the background, which would consume battery life.
Hope this helps.
Message was edited by: jia10