I don't know if you have a defective device but let me assure you, if you're going to have the camera in the background for an extended time it WILL get hot and the battery life WILL suck. Mine has no heating or draining issues but the camera is a powerful tool that does suck battery pretty heavily and does make the processor work. So really, IMO, if you actually close the camera and then you have normal temperatures and good battery there is no problem.
Understand what you are saying but the camera was only an example.
I had the issue with HERE maps in the background and also Facebook as well.
I have now updated to the official Update 1 of WP 8.1 and the issue seems to have gone away so far. I have left things in the background and the phone has not heated up at all. The battery drain under normal usage has also improve as well. Looks like they have change a bit of the scheduler in update 1 which has made this improvement.:smile:
I am continuing to monitor the situation and if anything changes I will post the result.