We had this exact problem twice with our 01.

First time around: Our regular dealer couldn't figure it out either. Tried a different one, and they got it on the first try. Thermostat and an ignition coil replaced at 35k miles. I believe the coil was replaced in the process of diagnosis (something for your techs to look at for sure), but the culprit was the tstat.

Second time around: Plugged crank vent line/oil-separator clogged.