Normally, those kinds of controls mechanically open or close a "bypass" valve in the engine coolant circuit that directs or prevents coolant flow into the heat exchanger that the AC/heater fan pulls air through. If the valve is completely closed, you get no heat. Completely open, full heat and in between, as it opens, increasing warmth mixed with whatever air is passing through.
The only way the PCM could affect this would be by it controlling a motor that regulated the valve, rather than having the mechanical linkage.
Now, climate control DOES use such a motor, so I wonder if Ford uses that kind of actuator on all trucks to simplify production, and, your knob regulates a voltage signal to that motor or something equivalent, which would have you manually doing what my PCM does.
If your truck is like mine, the center section of the instrument panel is dead simple to remove, so you could see if that knob has a mechanical or an electrical connection. Maybe the knob "signals" the PCM to adjust the valve?
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So, I was "thinking out loud" above. I looked at the wiring diagram for my model year truck and it appears Ford controls heat/cold with a "blend door" that is moved by a motor. There is always coolant going through the heat exchanger in this setup. So, for some reason, I guess your blend door is moving to full heat open as soon as you move the temperature knob off of full cold, or, the AC is completely cut off if the knob is off full cold.
And, the PCM is involved in this to a certain extent. Looks to me like it controls the AC clutch, although the diagram is not at all clear to me here. I don't see anything like a temperature control rheostat in the diagram. (It's probably "buried" in the Electronic Manual Temperature Control Module, which I think is the front of what you're looking at on the instrument panel, with the knobs - and it does NOT connect to the PCM. But it does control the blend door.)
That module has three wires going to the blend door actuator. The motor is positioned through a Dark Blue-Light Green and Orange pair and feedback on its position is through a Violet wire.
By now you must be hopelessly confused (I think I am).
So on the off chance that it helps, I'm including the three pages in the wiring manual that refer to a system like yours in the 2005 truck. Sorry about the quality. It's a scanned copy in a pdf file on my computer and I did a PrintScreen of the three pages that apply.
Oh, DO feel free to contact Bill directly on this. There are no "channels" here.
- Jack