Clutch chatter... cause and correction?

[jakeru]

Almost forgot to add... recently a couple times when the weather dipped below freezing, I noticed a sound similar to a noisy or chirping alternator belt on cold start-up, which went away a few minutes later after engine had warmed up. This noise would immediately go away when clutch pedal was pressed in, and come back as soon as the clutch pedal was released (until engine got a bit of warmth in it, in which case the noise would go away until the next below-freezing cold start). This was kind of perplexing, as it seems the transmission seemed to be making the noise? Not sure if it was related to the clutch chatter, but just in case it is, I thought I'd throw that in.

(Also, since I'm mentioning the transmission, I'll also add that it's hard to shift into gears when cold, and I have some new Porsche transmission fluid I'm planning to change whatever stuff is in there now, to hopefully fix that. When it gets warmed up, the transmission shifts nicely.)