Scenario 3: iPhone with non-fixable battery problem.
If your phone isn't running CPU-bound applications, and the steps in Scenario 2 didn't solve your problem with short battery life or a too-warm phone, then it is possible you have defective hardware. People are also reporting very warm phones, warm spots on the phone, spontaneous power shutdowns, and severe power drain caused by using the camera. Under such circumstances, it might be worth trying the "clean restore" technique described for Scenario 2.
If you simply need more battery power than the iPhone offers when it is running properly, watch for an upcoming BYTE review of battery cases that can add extra milliamp hours (mAh) to your phone. And please let us know if you've found other problems with the battery life or other ways to increase it.