Dang Sion, I thought I wrote long posts. Nice explanation. Very detailed and completely accurate.
You did forget one possibility, though: (technically 2, but they're both the same failure)
There are (on most cars) two valves that are moved by wires when you turn the temperature dial up. Depending on the car, the cables could be attached to the dial or the dial could activate motors that move the wires for you. Either way, the two valves are opened by wires. This is good because it lets you trace where the valves are. One will be inside, usually under the dash on the passenger side somewhere. The other will be outside on the upper heater hose. That one's the valve that directs coolant through the heater. If either one of these valves gets stuck, you won't have a properly working heater. Watch the valves as someone turns the dial. If they move, you're OK. If only one moves, fix the other one.
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