I've got the EXACT same problem. Unfortunately ... I was thinking about taking it into the dealer (1 month old, only 1200 miles on it) when I got rear-ended. So now my Cayman is stuck at the body shop for a very long long time.
Will you let me know if you find out what the problem is? Like yourself, I didn't notice anything wrong with the A/C functioning ... it seemed cold enough, but that sound was horribly loud and annoying.