Rather than starting a new thread I thought I would ask my question on my battery light issue here...

My battery light is on. Turning the key to on, but not starting, the battery was reading 11.69 volts. With engine running the alternator is putting out 13.78 +/- volts at 2500 RPM. So I assume the battery was shot so I replaced it.

Battery light is still on. When I pulled the engine cover off the right side over the alternator was very warm but the rest of the cover was not. There is a faint electrical or over heating smell coming from the alternator area. When I touched the alternator with a rag between it and my hand it was extremely hot.

Do I assume that even though the alternator is producing the normal charging volts per above that there is some other issue with it; bad bearing or some other alt component that is over heating and REPLACE the alt? Or are there any other reasons that the battery light would be still on after replacing the battery?