My two cents:
First of all, advices like "try disabling 3G, Wi-Fi, Bluetooth" are irrelevant, because each one of us know exactly how much our batteries used to last with the same setup in the previous version and how much they're lasting now.
When the bug first appeared in my case (after the OTA update from iOS 7.0.6 to iOS 7.1 in my iPhone 4s) I knew something went wrong because before the update I used to charge the phone once every two days (even when I used it heavily) and right after the update I was charging it twice a day, even on low usage. So then I went down to DuckDuckGo & Google and stumbled upon with this thread.
First, I followed the Lawrence's advice and completely restored my phone, it seemed to "fix" the issue, but the reality was it only made it less noticeable as after that process I had to charge the phone once a day only (Remember that right after the update I had to charge the phone twice a day but before the update I only used to charge it once every two days); And anyway, I was comfortable with that, a less noticeable (although existent) battery drain.
Then today, the bug "reappeared", the phone was overheatting and the battery was draining like crazy. I came back to the thread and read more:
Rndservices tells us that just by turning the phone off and then turning it back on (with all the apps closed and waiting 30 secs before turning it back on) the problem was solved for him.
brightblades recommended the usage of an app called "Battery Doctor" for memory cleaning, said that that was what solved the problem for him
And last but not "least", Lawrence Finch told us that the problem it's caused by a process that was interrupted during the update and now it's in a loop failing and failing.
With these 3 opinions, I was able to find a pattern:
Lawrence was right, the bug reappered for me today when I was using the phone and it suddenly shut down (because of the lack of battery) without properly closing some apps. After that, I plugged it to the computer for a charge and the result was a spinning wheel in the right side of the Wi-Fi indicator in the "home screen", (telling me that something was trying to refresh and failing a lot, as the wheel never dissappeared even after hours). Turning on Airplane mode cooled down the phone and helped it recharge, but turning Wi-Fi (or 3G) on again, caused the loop issue. I tried the Rndservices advice and turned off the phone. After turning it on again, the spinning wheel still was there. So I downloaded battery doctor and ran 2 memory reallocations. The problem was solved! No more spinning wheel, no more "burning phone". The battery drain stopped.
What I make out of this is that Rndservices was able to stop the problem with the turn it off/on approach because some services stop trying to refresh after a few failed attempts (or disconnection, so closing all the apps and turning airplane mode might have worked for him as well). Completely restoring the phone (as lawrence told us) works because the apps simply "dissapear from it" (and the loops stop, obviously) and the brightblades advice on battery doctor works because the app "kills" those rogue processes.
My other guess is that battery life will never be the same in iOS 7.1, as Apple marketed it as "a performance upgrade" and the devices really feel faster. It is possible then, that for this approach (and this could be a lie, as I'm not sure of my theory) Apple had chosen to increase the clock speed of the processors (which would led to a faster performance indeed, but at the cost of a bit of more energy hungry phone)...
However, even if my theory it's correct, we still have a battery drain bug as in iOS 7.0.6 we've never experienced "rogue background processes" (or at least I didn't), so Apple have to take a look at what's happening there.
