Just had this exact same issue with my '97 965: Screeching sound on start-up that gradually went away within 3-4 minutes. I thought it was the timing belt tensioner. It actually turned out to be one of the idler pullies on the timing belt. My mechanic showed it to me: it was almost completely siezed. His experience is when they finally go, they shatter or break and take the timing belt with them. Good-bye engine; hello $2000 engine and head re-build.

RUN don't walk to your mechanic and get this checked out ASAP. This crummy little $30 part could have ruined my perfectly good sub-100K mile engine.