Deggie, you appear to be an experienced knowledgable poster from your self-assured tone, however I think you do not understand the problem that most here are describing. Your posted link above refers to a problem identified prior to 6.1.1 and related to exchange server; that is not the cause of this particular problem, which has only started to occur since 6.1.1. For a definitive diagnosis of the current problem, check Settings, General, Usage and near the bottom look at the stats for usage time versus standby time (see svr43 screen above, that shows a wide separation between standby, usage -that's good). They should NOT be the same, if the phone is working properly. If they are the same this indicates that the phone is constantly engaging the processor so that in effect there is NO idle standby time. And thus usage and standby (idle) time are the same. The result of this continuous usage leads to high demand on the battery with rapid depletion and producing excessive heat, enough to make the case noticeably warm to touch.
My 4s was running 6.1 until Feb 11 and it only required a charge about every 1 and 1/2 days, and never overheated, and had a large difference between standby time and usage time. On Feb 11 after prompting from apple via notice appearing on my Apps Icon alerting the need for an update, I did that. Over the next few days I noticed that battery life was reduced to approximately five hours from typically previous 30 hours. Yesterday (14) I noticed the case was warm to touch, it had never before exhibited that. Thence attempting to diagnose why these two Things were occurring I started to notice the highly unusual stats about usage versus standby. After going through several recharge cycles each time this relationship has persisted. I do not use exchange server, it is not invoked on my phone. There have been no other changes in my usage patterns or applications over the past month.
A friend told me this eve that he had a similiar problem starting on Feb 12 after updating. Same symptoms and usage stats as I've described. Apple Store worked on his phone for two hours, did a number of backups, resets, etc and pronounced it fixed but refused to tell him what the cause was. His phone has been acting normally for past two days. This is not related to exchange, nor an application program problem This is a problem caused by 6.1.1 inside the core firmware and can only be remedied by apple, either thru hands on servicing or perhaps a fix to 6.1.1. I have not been on this site before but need to travel tomorrow and thus cant avail myself of a vist to Apple store. So came here expecting to receive REAL support from Apple. I have not found anything useful from Apple, only ignorance and stonewalling and misleading advice from Apple apologists. Apple should be able to do better for its customers.
M