I picked up a new 7 Plus and have been setting it up and playing around with it for a few hours. On the back lower left side, gets kind of warm... Other than that it works great! I wanted to check to see if this is normal or not. I figure if it isn't I can exchange it, and if it is I will need to decide if it's enough to warrant a return.
In Portrait mode mine gets warm on the left side. I actually had one originally that got noticeably warm, but the second one doesn't get that warm at all, though it has the SOD issue and 3 dead pixels in it.