Mine did the same thing. It was the Temperature control switch (not the actual name)located inside the engine bay. It is mounted to the airbox just to the left of the Transmission dipstick as you face the the vehicle.
do you inform me better about to find the Temperature control switch? also my Town Car 2001 don't fan go, the blowermotor is ok but don't start the fan also if is in max. email@example.com from Italy
I had the same problem on my 99TC. The fix for me was:
With a screwdriver, tap on the fan control modual. The modual is in the engine compartment, left side as you face the engine, mounted on the air box and behind the valve cover. The modual has a red and white sticker. Kinda hard to see.