Here is a 4100 C4AF-DH, FORD PART NUMBER C3AZ-9510-AK.
I am not a carburetor specialist so when I go through a unit I make an effort to understand the operation and test as many circuits as possible.
In the sixties there was a problem with fuel percolating out of the carb and flooding the engine in hot weather. Perhaps the reid vapor pressure of straight run gasoline of the era was partly to blame, I don't know.
I noticed the idle compensator valve and traced the circuit. It seemed to me that it would begin to open at 135F and fully open at 195F when a car was turned off in hot weather when heat soak would boil off the fuel in the float bowl and flood the engine upon a restarting the vehicle.
The purpose of the valve as I see it is as follows.
1. Open and help vent the vapors of the raw fuel to the air cleaner as it changes state in the intake manifold when the car was turned off and sat in the parking lot.
2. It would remain open when the car is started to add additional air to lean out the now, very rich, air fuel ratio. The airflow of the running engine would cool the valve well below the 135F to 195F where it opened and close it.
It doesn't make sense that it would open when the engine is running to cool it off. Not to me anyway.
First of all, the additional air would lean out the engine since the air is coming straight down a non metered hole which would make the engine run even hotter, some of the cooling effect of the fuel is removed in the now lean condition.
In addition, speeding the engine up to cool it off is like a dog chasing it's tale. The engine is burning more fuel and the automatic transmission is engaging creating a load and more heat to the cooler which is in the radiator. Advancing the timing would do a much better job of removing heat.
Lastly, the valve on my carburetor begins to open at 135F and is fully open at 195F. A running engine is pulling in outside air which is partially heated by the engine compartment, but should be well below 135F. If this valve was designed as a hot idle increaser the control range would need to be much closer to avoid nuisance leaks. If a engine is overheating or is in danger of overheating, this little valve isn't going to do anything to help the situation.