If you have had your lincoln at the dealer for this problem before,and they worked on it, I would take it back to them and tell them they did not repair the problem.
how did they check the water pump, if the impellers are coroded off the shaft, the only way to make sure it is still good is to remove it from the car, i've been reading about customers with water pump problems and cooling fan problems.
and to answer ase_master327's question.
the lincoln LS has 2 seperate heater cores, 2 seperate ac evaporator cores, 2 hot water control valves(with 8 hoses coming off of it),a thermostat, radiator, 2 seperate cooling system air bleeders, several cooling system bipass hoses, and a cooling fan that runs off of power steering fluid.
just running the heater will not get the air out of this system,....believe me!!!