I had a similar problem with my iPhone 5. After functioning normally for several months since purchase, yesterday it began demonstrating rapid battery depletion, around 20% per hour despite being asleep in my pocket. It was pretty warm, too. Turning off all apps did not help. Placing it in airplane mode stopped the depletion but obviously was not a good long term solution. Multiple resets had no effect. I tried disabling cloud services but that did not impact the battery drain in my case. I'm not sure how to check error logs, but that might have been helpful. Eventually, I found Mail was attempting to send two emails I had written the night before and appeared to be stuck in the process. The little circle in the top bar on the screen indicating activity was constant and a progress bar at the bottom appeared stuck. This was only evident when I had the Mail app open and 2 resets did not appear to correct this (I didn't discover this issue until after 2 resets).
I turned off Mail in the Settings and later turned it back on. Mail then functioned normally, no more constant spinning activity circle and the progress bar was gone and the out box was empty. More importantly, the rapid battery drain was completely fixed and the phone cooled down.
After my experience and reading your post and others, I suspect this rapid battery depletion can occur when the device gets stuck in a process (forgive my layman's terms). Unfortunately, it appears that a system reset does not always resolve the issue. iCloud and Mail are good places to look for the issue. If you can pull up the device's error log, that may help as well..