of absolutely flawless reliability (and 1 month after my warranty ran out

) I have a situation that makes the bike useless. What I have: a 2002 M620.
The problem: The battery is being drained while I am riding. Once I arrive at my destination after about 60 miles and turn the engine off, I get that 'wonderful'

'click' 'click' sound when trying to start again.
What I do know: The alternator is functioning/charging during the full rpm range. The battery is fine; after the problem first appeared I bought a new battery. I can tell to some extent when there is almost no current in the battery left to start the bike: the idle speed is slightly under a 1000, as apposed to when the battery is fully charged it is slightly above a 1000. Also, this maybe more my imagination, but it seems to drain faster when the temperature is warmer; afternoon ride vs. early morning ride.
The question: How does one trace/investigate the source of this particular problem?
Where's the first place I should be looking at.