When the ambient underhood temp increases to a certain point the bi-metalic strip on the hot idle compensator opens a rubber needle - brass seat metered orifice, causing what is essentially a vacuum leak of a predetermined amount into the intake system. This extra air will in turn cause the idle speed to increase, moving more air through the radiator and water through the cooling system due to increased fan and water pump speed the result being the motor will cool down to the point where the ambient underhood temp is lower, and the valve closes and the vacuum leak will stop, returning the engine to a normal idle speed. This cycle repeats itself over and over. Obviously this will only help during periods of engine idle . Remember, this was engineered in the early sixties and in theory is workable. What normally happened is that IF the little rubber needle valve did lift from the brass seat and cause the idle to increase, it sometimes would not seat properly when cooler, and caused an eratic idle. Most were tossed in the garbage back in the day. In the real word this little device probably caused more problems than it solved! It had a somewhat short life, was kind of a band-aid fix, and was replaced with a bigger and better cooling system as more and more Fords products were sold with factory AC. I do not remember the idle speed increasing in proportion to the temp.
