Battery issue with my iPhone 3G 16GB. Unlocked and jailbroken.

Over the last few months, Iíve been having big battery issues. It will go from a 100% charge to powering down in just a couple minutes of use; apps and email. Hereís the thing. I got a battery tracker and started experimenting. If it dies, I can let it sit for five minutes and suddenly Iím back up to 80% power or so. Iíve also seen it sit idle and go from 40% and ďcharge itselfĒ unplugged back up to 100%. It also mainly does it when Iím putting it through some heavier use like surfing and so forth. If I just use the iPod, it slowly discharges but I can get the ďunpluggedĒ charging if I let it sit again.

I believe itís heat related. I can feel the phone get warm, but not as hot as it used to when I first updated it a year ago or so.

Things Iíve tried. This phone was unlocked and jailbroken ages ago (actually it was originally a hardware sim card hack). It had the battery issue, so I updated it once, did the software hack and havenít done it again since the 3.0 OSís were released. Because it solved the problem before, over the weekend I updated to 3.1.2 and baseband 4.26.08. Prior it was on the 2.XX OS and baseband 2.24.00(?). I was hoping this would fix the battery issue.... but it did not.

Would replacing the battery be worth it and fix the issue?