I had the battery and the heat problem too after installing 6.1 on my iphone5
In the same apple community forum the proposed solution was to drop/add Exchange account. That helped. I don't even loose single percent overnight.
Wall Street obviously believes that the days of making money on hardware will soon be over. They want to see a recurrent revenue model (this is why they LOVE Google and especially Amazon with 1300+ PE ratio ). Maybe they are right but they are betting on it too soon I think. In the mean time Apple should think how to spend their billions to turn the ecosystem into a money making business.
And it won't even end up with this. Eventually I believe Google will even pay you to get a phone or a tablet (for example in a form of free or discounted Data access, Amazon does it already though Kindle's price is still above $0)