(1) Just on the original battery, 1 year of good battery life may be reasonable given your usage, or not. If you routinely run the battery down all the way before recharing, the quicker you will wear out the battery. If you let it get hot, say leaving in a hot vehicle, likewise.

(2) Given the situation with the second battery, it would seem there is less reason to think battery #1 was just worn out. However, is the second battery a genuine BlackBerry battery? Did you get it from a reputable source? Have you been able to try it (as well as battery #1) in another BlackBerry?

(3) Are you sure nothing besides the four or five core apps is running? Do you have anything set to run in the background, anything that updates frequently? I would check every app and look at the settings.... Just because you don't see an app in the switch applications screen doesn't necessarily mean anything.

(4) The device surface can get warm to the touch sometimes, depending. But only warm. If it is hot to the degree that you find it painful to hold, I would say there is definitely a problem with either the device or the battery.