The heater is blowing constant hot air even if you put the temp control on cold. Is this the heater blendor motor and where is it located?

There's always the divert-er valve that opens and closes the hot water flow to the heater core. I'd say a serious obstruction in the radiator but you'd be overheating and seizing the engine as well. Did a previous owner by pass the heater?

you have a leak in the vaccum line,or the heater control switch is suck.

could be air in the system or the thermostat could be in up sidedown .

The doors that open and close in the heater control unit are ran by motors. It sounds like a motor has quit in yours. When turning on the defrosters the motor closes the door to the heat for the floor

sounds like the blend door motro may be bad, this motor is screwed to heater box, there are a few of these motors one for pass/side for hot/cold air then one to control position of air like defrost or vent or floor, then the driverside cold/hot air, i think this motor is on driverside part of heater box, to make sure locate each motor while moving all controls until you spot the one that doesnt move, then remove it and move door manualy to see if you get heat, then replace that motor, hope this helps,

i've been down here too myself, and discovered that the temp control motor, located in the bottom of the glove box, which you can access by clearing all your stuff in in and opening a small door.
you can adjust it manually, and see if it changes, if yes, the switch can be defective, as well as the motor, the switch is the most likely problem.
but adjust it manually first.

Phil
grandmotors.ca

After warmup it still blows cold, or only when cold? Normally the fan will operate independently of engine temp except in some climate controlled vehicles. As long as it blows warm air after engine is at temp that's a good thing. the heater uses hot water from the engine. Obviously the heater can't be warm before the engine is. If it's cold after the engine is hot, there are vacuum controlled "motors" on top of the heater box under the dash that move doors that control heat. Either one of the control motors or one of the doors have stuck or failed. Many also have a control valve on one of the heater hoses under the hood as well. If the engine comes up to temp then the thermostat is good (should be at about 210f) Only remaining item is the core itself which may be internally or externally obstructed.
All this being said, if it's good when the engine is up to temp, leave it alone...it's fine.

Your problem is a faulty heater control valve. The design used on these vehicles allows for hot water to flow constantly and compete with the evaporator as there is no blender door. You have to replace the valve and possibly the control head. Meanwhile, you can bypass the valve to have cold air

I know this problem all to well as i am a Ford dealer tech, the problem is caused by either a defectice air temp control blend door actuator motor or a stuck air temp control blend door or in rare cases both, your system's door is stuck n the heater position, which is where they almost always fail.

Taurus does not use a heater control valve. It runs coolant thru the heater core constantly. You may have a temp blend door actuator problem or a plugged up heater core is also very common. Feel the heater hoses, they should both be very hot, it one is much cooler; you can try to back flush the core.