NO HEATER OPERATION?

There is no quicker way, it is a 1 day job no way of getting around it.

to verify it is that, you should feel the heater core hoses, if both are hot, then it is the box, if one or none is hot then it isn't the air ducts.

are they doing the heater core ?
if its the blend door
i would check the actuator
get a diff opinion and estimate

I think you should find the thermostat and replace it and check for clogging heater hose and heater core for a start. Do you feel any warm air at the passenger side near the blower motor or any warm air at all.

and this guide and video can help.

https://www.2carpros.com/articles/car-heater-not-working

and

https://youtu.be/SNRb6pSwYuU

Check out the diagrams (Below). Please let us know what happens.

The clicking sound is coming from the blend air door. The door moves direction to allow heat into the vehicle. If it is stuck, you will only get outside air. Check that and let me know what you find.

Joe

Check the thermostat and then have it pressure tested to find our more what's going on

For 4.0 Liter

The thermostat is located where the radiator hose meets the engine.
Old engine image by John Sfondilias from Fotolia. Com
The engine coolant thermostat acts as a gateway in the cooling system to allow or disallow the passage of engine coolant through the engine. To run optimally, the engine on your Ford Explorer needs to maintain a constant temperature, give or take 10 degrees. The thermostat closes when the engine temperature drops below that threshold and opens when it rises above it. Unfortunately, thermostats are not made to last forever and should be replaced during every cooling system repair. Make sure the engine is cold before beginning any cooling syst
Place the drain pan beneath the engine, below the thermostat housing. Locate the thermostat housing by following the upper radiator hose from the radiator to the housing.

Use the socket set to loosen the hose clamp on the upper radiator hose and then pull the hose off the thermostat housing by hand. Aim the hose down toward the drip pan to catch any coolant that may escape.

Use the socket set to remove the two bolts that hold the thermostat housing to the top of the engine. Lift the housing off by hand. Inspect it to make sure it has no signs of corrosion; set it aside. If there is any corrosion, you will need to replace the housing.

Pull the thermostat out of the well in the top of the engine. If it is stuck, you can use the pocket screwdriver to lift it out. Either way, it should come out easily. Note how the thermostat was positioned and oriented in the well for reference during installation.

Here is a picture guide as well

https://www.2carpros.com/articles/replace-thermostat

And https://www.2carpros.com/articles/car-heater-not-working

If it has a heater control valve check it and make sure the heater core is not clogged-up further could be one of the following below

Air mix/blend/mode/ recirc door problems and vacuum/actuiators and HVAC control module

IS the coolant full? Also, try this. Start the engine, let it warm up with the heater on high. After it is warm, with it still running and the heater still on, feel both heater core hoses. Both should be hot. Let me know what you find.

Joe

With the engine warm and the heater on, check to see if both heater core hoses at the fire wall are hot. Let me know what you find.

When you say the AC is on, is the AC compressor running? Also, with the engine hot, running, and the heater on high, do both heater core hoses get hot?