2001 ford Taurus 3.0 over heating no heat change water pump

The heater core might have a blockage or the inlet water valve may be stuck. The thermostat on the engine may be stuck open as well.

Front seal. Had a 95 taurus do the same thing.

possibly the bled door is stuck open so only the cold air from a/c works when on defrost vs closing to allow heat to cycle through the system as defrost runs through the a/c system

If both heater hoses are getting hot, the problem could be a stuck blend door under the dash.
If only one hose is getting hot, there is a blockage in the coolant flow somewhere.

heat control valvue could be stuck closed not allowing water to pass through the heater core

Either the water pump not working,,or you have a clogg some where..I have seen the impellor break on the water pump..The outside pulley was turning but the inside wasnt..

You need to check if your fans are coming on. Start the car, turn on the A/C pop the hood and atleast one fan shoud be on.

Start the engine when cool, remove rad cap and start engine and let it run with the heater on. (not defrost) Top up coolant as needed in rad, and let it run until either the rad fan comes on and off 2 or 3 times, or you can see increased flow in rad from thermostat opening. It will obviously happen after it reaches operating temperature, so watch after gauge gets close to there. Wait until you see that flow 2 or 3 times or fan comes on and off before you put cap on, and fill return bottle to proper level as well. That should cure it, by getting air out of system, and coolant flowing through heater core.

Sounds like a stuck thermostat no heat water not circulating to heater core engine overheats stuck thermostat won't let water circulate through engine

Check your coolant level. If the antifreeze is low the water pump may not be able to pump enough of the coolant through your heater core. When the car runs faster it is able to pump more of the warm antifreeze to the heater core.