2000 Lincoln LS Relay/Cooling Fan

Your alternator wouldn't cause your car to overheat.
And your car only uses the fans to cool the radiator while you are sitting still. At speed, your radiator is cooled by air flowing through the front of your car.

When do you most often experience your overheating problem??? And if you are overheating but your fans are only turning slowly, then there definitely is a problem. If you're familiar with a DVOM, then you can use that to test your fan relay and the motor windings of the fan. Also check the wiring/connectors for looseness/corrosion.

If you're experiencing overheating at speed, then this won't be your fans. You'll have to have your cooling system diagnosed for other issues. Since you've already replaced the therm, and water pump, you'll have to check your radiator/heater core/engine block for a blockage.

If your system checks out, then you'll be looking for a blown intake/head gasket.

Thank You Ernest for responding. It only overheats in stop and go traffic and only when I am not running the Heater. When I run the heater it is not running hot as per temperature gauge. I have had a power steering problems and need to have a Power steering pump replaced and I am quite sure that that the hydraulic fan in said car runs off the pump . I will clean the fan for any corrosion first because of the original leak in the power steering problems may have disrupted the motion of the fan. It is very greasy under the hood near the pump. Hydraulic Fan Assembly from Ford is 576.00. I priced the motor only it is 541.00. UGH !!