only if the thermostat is stuck open or has been removed
Your heater hoses are failing and they are located at the rear of the engine. They go through the fire wall into the heater core which is what the air blows through to heat the cab.
Which engine, V6 or 1.8T?
Actually, both are used. However, it is more common to pull air through the radiator towards the engine. This draws cooler outside air through the radiator. Pushing air from the engine towards the radiator means that you are pulling hot air from around the engine towards the radiator.
As coolant cycles through the engine, it absorbs heat from the engine, after which, it continues through the cooling system back to the radiator. As the coolant passes through the radiator, the heat is exchanged to the ambient air by way of airflow through the radiator fins (this is why it's important not to bend the radiator fins).
You most likely have a blown headgasket.
A car's radiator is used to help keep the engine cool. During operation, an engine's moving parts create friction, which produces heat. Coolant flows through the engine picking up that head and travels back to the radiator where it is cooled down by air flowing through the radiator coils. The cool coolant then travels back through the engine completing the cycle over and over.
An engine flush can be done by draining the coolant system. Disconnect the top and bottom radiator hoses, and keep filling the top hose outlet with the engine running, allowing the water to run through and flush the system. Take care to not run the engine too long or it will overheat.
Add coolant, with a cold engine for safety, through the "radiator" cap in the upper hose.Add coolant, with a cold engine for safety, through the "radiator" cap in the upper hose.
The radiator on a 1999 Mercury Cougar is flushed by draining the radiator, filling it with water, and adding a commercially available radiator flush. The engine is allowed to circulate for 10 minutes, drained, flushed with fresh water, and refilled with coolant.
The water pump humps cool water from the radiator through the engine. Hot water. Leaves the engine and enters the top of the radiator. The hot water works its way through the radiator cooling itself.
In radiator or through coolant recovery tank
The water pump.