ipad2 random temperature warnings after 8.3 update

iPad 2 rev A (16G and wi-fi only) exhibits random shutdown due to temperature warning after I updated it to 8.3. The unit can play a movie for a couple of hours fine, sit at idle all night long or just as easily fail after being on for just a couple of minutes after sitting all night. Ambient room temperature is about 20C and unit is not in direct sunlight. As I write this I had the app BMSSM running (about 10 minutes or so) which was displaying a CPU usage of 8-10% when a temp warning was activated. Does not seem related to the running of any particular app and occurs whether wi-fi and/or bluetooth are up and running or not. Interestingly, battery takes quite a bit to come off 100% but once battery is below about 45% it falls off fairly quickly (say 45 to 20% after only a couple of hours of just idling.

A simple restart will bring the unit back up and it may fail within a few minutes or quite some time later. Have gone tthru the various recovery, restore and DFU procedures with no luck. Can't recall ever conditioning the battery so I've taken it down to low battery shutoff and full charge once now and am in the process of trying to bring it down to shutoff again.

Of course, it just came off AppleCare a couple of months ago so now I'm on my own. Any suggestions? Possible battery problem maybe?

Thanks