takes 15-20 minutes before a/c on 2003 Lincoln TC begins cooling

The AC system may just need a charge. Take it to a shop that does this, and have it checked out.

I should have added that the a/c works fine, blows cold, once it starts working. Suspect the problem lies in the a/c evaporator air temperature sensor, a $20 part, but a 5-hour job to access involving dismantling the dashboard. There is a quick fix on the internet which bypasses the EATC, but it is for a Ford Fusion. I do not know how it would work for my 2003 lincoln TC.

I wonder if a bad blend door actuator could cause this? It is a very expensive repair due to the labor involved. If this is the problem make sure the repair is done with a genuine Ford / Lincoln part or you may be soon doing it again.