surgicalspirit and holdrege, I have to concur with this resolution, and I'm frustrated as to why it worked!
I was so ready to look at other smartphone providers.
We don't have LTE in NZ, so I knew I didn't have that specific issue, I tried turning on and off everything that has been mentioned in this thread and nothing seemed to solve the issue.
When I purchased the iPhone 5, I set this up as a new iphone 5 (although I can't remember whether I had 6.0.1 or 2). But, I did restore everything from icloud from my iPhone 4.
Anyway, last night I had had enough. I decided to do a full restore (Erase all Content and Settings), set the iphone up as new, and only use my apple ID to sign in and activate. Did not use iCloud as part of the activation process. As soon as the phone restored, I deleted the icloud account that was setup as part of the activation process which was my apple id (I use an *Me.com icloud account, but a @gmail.com apple id).
After it was setup, I then synced all my apps again from iTunes (connected). And only then did I activate the correct icloud. I also set iPhone Backup to Computer, NOT iCloud like I has my phone set to before.
I am at 77% remaining and my usage today was very typical of what I use to do on my iphone 4.
No doubt about it, iPhone 5 is going to use more juice because of it's capability. But, I am really at a loss for words as to why this full wipe and setup "as new" worked. But it worked. And it worked exceptionally well, and like others, this has solved the badly overheating battery issue....
And I am one very very happy apple user again today...! 🙂