This will be long. The plastic fan bit relates to the water pump that pumps the coolant throughout your car's cooling system. It has what is called an impeller (Like fan blades) and in the Contour it is made of plastic. For some odd reason, Ford decided to be cheap (What a surprise) and used a weak plastic impeller, and the blades would break. No impeller means very little coolant circulation if at all. The big problem people have is that it's very had to diagnose because these things don't usually happen to normal cars. It mainly happens on Duratecs, but I imagine the Zetec has the same impeller. Someone can chime in on that.
It's quite obvious when a car is overheating to me. Whenever my girlfriend's Caprice would over-heat, there would be a nice cloud of steam rising from the motor. Took me forever to find the source. Found out that the thermostat was bad and that caused the intake manifold gasket to break.
Overheating is usually a bad thermostat. This piece starts off closed to keep the coolant re-circulating throughout the engine to help heat the motor up quickly, and then it opens around 180 degrees to let the very warm coolant filter into the radiator (Note the coolant has only been circuling through the engine block where it cannot cool down) where it will be cooled off before entering the motor again.
Your fan helps the radiator cool the coolant down by blowing air over the radiator fins. Rear-drive cars usually have the fan directly attached to the motor (Because the engine is pointed from front to back, not sideays like in your car the fan can directly attach to the crankshaft of the motor. This crankshaft is what is being turned by the pistons) and there is usually a viscous "clutch" to either let the fan slip when temperatures are cold, or it will attach the fan directly to the motor and it will spin.
Unless you're driving a Chrysler LHS car in which the engine is in fact front to back but the car is front-drive, there is no simple way to attach the fan to the crankshaft since it is pointing towards the side of the car. I have never seen a car with fans on the sides of the car. In this case, the fan has a seperate electric motor to drive it. This is controlled by the car's computer brain (PCM) and switched on when the temperature rises above a certain level. Sometimes the fan does not turn on, or the coolant sensor goes bad. All you need to do is open the hood and switch on the air conditioner. The AC system automatically turns the fan on no matter what. If it doesn't turn on...we got a problem.
Letting your engine over-heat is NOT a good thing. You need to find out what's wrong quickly. If you really must drive with it like this, turn your heater on full blast. The heater core will bring the hot air into your car from the engine. Just make sure your windows are down and the vents are pointed outside the car...driving like this in the middle of 100 degree sunny weather was not fun at all. Don't let this happen to you!