I've seen a few similar posts, and wanted to add mine to the discussion. Just within the past week, my Droid Razr M began overheating and the battery began discharging within an hour or two.
I have gone through all the steps suggested by VZW customer care folks. I have read thru every similar post that I can find. None of my usage behavior has changed - I make calls, play a little backgammon, and use Navigation about once weekly.
The Battery usage app shows the display as chewing up the vast majority of the battery power. There are no rogue apps found. I close out/shut down every app as soon as I'm done with it - I don't leave anything running in the background if it can be turned off. I even check to see if anything's running after every call.
Bottom line: The phone suddenly began overheating, which is a symptom regularly associated with increased load and/or battery discharge and failure. Given that there have been no changes in phone workloads, I'm guessing it's a battery issue.
What does anyone else think? And is there anything that anyone has tried that works to increase battery life in this situation?