[95avblm3]

Going out on a limb here...

Is there any chance it is a fastener or hose clamp either loose or not that may have gotten moved or otherwise placed in close proximity to some other vibrating part? I'm thinking like a heatshield or something... related only to the movement of the engine by the vibrations caused by the engine. Perhaps is comes and goes only when the engine is warm due to thermal expansion... when cold, it can't contact and when it is hot, it moves beyond being able to contact.

What is the condition of the engine and transaxle mounts? If they are worn or loose, that may explain how engaging/disengaging the clutch may be affecting it.

This may be completely off base but it may be worth looking at everything around the engine and not just the engine, itself.