Bobby 5/19/2010didn't believe you at first when you said hydraulic coolant fan! but did some research and yes the lincoln ls 2000-2002 has a hydraulic fan, also found out they had some problems with them and this intermittent overheating problem could be related. what you need to do is when the car is overheating check to see if the fan is spinning.
Another note something i just learned the hydraulic assembly works off an electronic accuator mounted to the pump that regulates the flow of hydraulic fluid to the fan to control its speed. there could possibly be the problem. there was also a tsb on this issue
TSB Number: 996800