I've had this issue myself, im on an iPhone 3G running 3.1.2.
This used to happen frequently when i first got my phone, but since doing a procedure similar to that outlined above(reinstall) the problem was gone, until it happened today. The phone got warm and the battery dropped fast, almost ticking down as i looked. Tried cold reboot, didnt fix it. Problem went away by itself after a short while. Next time i will check running processes.
Oddly, the iPod app likes to start itself up in the background, im not sure why. This happened even when there werent any songs on the device. It seems to happen more when running other apps which use audio such as ooTunes. Anyone else had this problem or have any ideas on the reason?
I'd like to point out something regarding downgrades of iOS. On older hardware, such as the 3G, it's actually perfectly possible to downgrade the OS using just iTunes. This is because that particular model doesnt require the UDID-based firmware signatures that newer hardware requires for any upgrade/downgrade(called SHSH blobs by JB-aficionados).
However, on a 3G, if you have at some point had a newer iOS on it, and through that upgraded your modem baseband, that part will not downgrade, and will give you an error at the end of the restore procedure in iTunes. At this point the device is actually successfully flashed with whatever version you chose to flash onto it(Hold option while pressing Restore) it's just the final procedure to kick the device out of recovery mode that doesnt get done when iTunes errors out. This is verified on iTunes 9.2 and 9.2.1, YMMV, especially on iTunes 10.
So, you will need a 3rd party tool, but only to kick your device out of recovery(and no information is ever in jeopardy, provided you chose Restore in iTunes).
On 3GS and newer hardware, its also possible to downgrade, but you will need a 3rd party tool which pretends to be Apple's servers, and you will need your signatures(easily obtainable whenever your iDevice was at the desired iOS version).
Slightly OT, but at least i got a few on-topic bits in