There is absolutely NO WAY this is related to cellular signal.
Let's apply critical thinking skills to the problem and see what we come up with! 😉
1) I have been using the phone in the same places every single day since I bought the phone in September 2011.
2) I have not ADDED or REMOVED any apps to the phone in over a month.
3) The problem STARTED immediately after I installed iOS 6.1 two days ago.
4) When I removed the Exchange e-mail account, the problem stopped.
5) When I added the Exchange e-mail account back, the problem reappeared.
I have tested this problem on WiFi ONLY. On cellular signal ONLY. With both connections on. It is still there.
I have disconnected calendar - contacts - notes - reminders - everything in varying degrees.
The overheating and battery life issue ONLY occurs with the Exchange account added.
It DID NOT appear until I upgraded to iOS 6.1.
Simple and easy deductive reasoning would indicate the issue is related to a problem with the iOS software. I have been operating, programming, tinkering with, experimenting and hacking on computers for OVER 30 years. I can program in 6 different languages. There is NOT a computer on earth that intimidates me. What is FRUSTRATING is to have a "world class" outfit like Apple out there ignoring their customers. 😐
So...I will continue to try and fix this problem on my own because that is the kind of person I am. If I find the right combination of moves that will make this go away...I will post it here for everyone.