2005 Mercury Grand Marquis LS Transmission

On first start of the day (engine cold), the transmission emits a siren-like sound similar to a hydraulic pump air-bound or cavitating. Sound disappears after first 1 or 2 miles of driving. Does not repeat during the rest of day when engine is warm. Repeats again at first start each morning. Ford dealer check of no value since mechanic could hear nothing with engine warmed up.
Any diagnosis suggestions out there? Thanks.

You could ask them if they can check it “first thing in the morning”, and leave it parked there overnight. If you have a second car (or can get a ride), go back to be there in the morning, when it’s cold.