2005 linc ls heater stays on full heat

Question edited for clarity and added a bit of punctuation.

First make sure the coolant system is full by removing the radiator cap, as opposed to the expansion bottle.

Part of the job of the blend door actuators is to cut off airflow from the heater core and only allow air in from outside. They would be the first thing to check.

https://www.google.com/search?q=2005+chevy+malibu+heater+not+working

https://www.google.com/search?q=2005+chevy+malibu+blend+door+actuator+location

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You must wait for the thermostat to open up, crank your heater on full, you will get only cold air once the thermostat opens it will start to heat up, heather runing wait for thermostat to open youll see your coolant bottle bubble up and go down , then you loosen the bleeding valve if you got one, cooling system service should be done all together , change thermostat,flush the coolant system, replace hoses if needed, if thermostat is shut and wont open up your more likely will blow a hose from the pressure .ty

It would indicate a bad hot water valve on the hoses connected to the heater core.

If your talking about the heat inside the car, yes. It is vacuum operated. On the passenger side. The hoses are about 1 inch in diameter. The valve is spliced in one of them. Make sure the vacuum is present before replacing.

The heater control valve restricts hot coolant from flowing thru the heater core when the air cond is running.
Usually if it fails, you have no heat.

Thermostat has nothing to do with the heat

You have a coolant control valve down low under
the a/c drier on the passenger side, bolted to the
radiator shroud

I have that car,very complicated vehicle,one of the
most high tech ford has every made

Beside that valve there are several other possiblities,
mostly all electronic

Need the experience & all the diagnostic manuals or
I hate to say it,but maybe a dealer,not many shops will
work on a ford or an LS

Check the 'heater control valve,' which is attached to the heater hose line under the hood. If it is malfunctioning, it will prevent hot coolant from reaching the heater core, with the result being no heat. This is a $30 part, usually not too tough to get at, although I've never changed one on a Lincoln.

The message means the electric park brake needs serviced. In this case I feel that considering the ac problem, the Coolant Control Valve is defective. The valve can create RF interference that messes with the electronics of the park brake system. The Coolant Control Valve is located at the right side bottom of the radiator fan shroud and has 3 heater hoses connected to it.

right beside the degas bottle top thare is a black hose sticking out that has a screw in plug in it that can be removed with a straight screw driver. remove this plug and start vehicle and let it run with heat wide open and on high till a STEADY stream of coolant is presant then replace plug - dont over tighten. this bleeds the heater core.

maybe you won't need to. On the fire wall you will see 2 hoses an inlet and an outlet.that go directly into the heater core. Sometimes the heater core is clogged. disconnect the hoses and use a water hose running at only a moderate flow. put it into one of the the inlet of the heater core and run water until you see clear coolant. Then do it on the outlet and run it until the coolant is clear. you are trying to remove any clogs the heater may have. if this does not work, check the heater control valve.move the temperature slider the one to control the temp inside the car. and see if you can hear anything move. Check to see what type it is it can be a vacuum controled vavle, or a cable hooked on to the valve or an electronic controled valve. if it is a vacuum controled valve, you can check to see if a vacuume hose is disconnected, if it is a cable type valve,check it by moving the temperature control inside the car open it and close it with your fingers if you can see it. But most likely it may be the heater core thats clogged.