If your car was severly overheating from a water pump not working, there would be paint chips flying off the top of hood, happened to my car, the one before my Contour, it was a 1990 Camry, it took a while to realzie it to, but by then the engine was wrecked, so that car was junk.
I would check other components of the cooling system, like thermestat, have you ahd the coolant completly drained and filled lately?????, liek within two years or 24,000 miles.
With your car running rough for a minute or two, does it do this in the morning, that is when mine does it, they all do.
When your water pump goes, either one of two things can happen, it will leak, or it will seize up and blow the bearings, and make metal fly and destroy the radiator and cooling fan, and maybe a few other things.
On this Contour to be safe I will replace the water pump at 60,000 miles when I get the timing belt redone, I have yet to get it done because my Contour just hit 53,500 today.
Now with your heater, you do realize that is under warrenty for 10 years or 150,000 miles right? The heater blowers have found to be bad from the beginning so they are under warrenty, tomorrow drive it to the Ford dealership tell them hey fix this, and it is 100% free.