Appologies for the late response. This really sounds like moisture built up on one of the belt pullies. Have you had any rain or drive through a pudle, or have some high humidity prior to startup on these occassions? Thats my first thought.

Another thought is a belt may be a little too tight or loose following one of the above mentioned events.

Lastly, I'm wondering about the timing belt you said was replaced. That wouldn't be slipping obviously, but if there is too much tension after install, there could "possibly", however doubtful, but not impossible, be some squelching, howling, squealing at times. I had an '91 Hyundai Scoupe that did just that after a timing belt install. Very rare, but it happened to me! Like I said, this is highly unlikely though.

It is possible, that a pully is in need of being replaced, but this would be a daily problem, or happen every time you have dampness or moisture in the air.