I think dakine858 is confusing this with the flap in the air cleaner which is what was described. Every car with the big blue air cleaner had a flap, only some cars had the hot idle compensator.
The hot idle compensator is similar only it works almost the opposite. As the name implies, the valve only works at HOT idle. The valve has a bimetallic strip that should hold the valve closed when cold and it opens when the car is hot, the fuel is vaporizing more and making the idle mixture so rich that the car doesn't want to idle. The valve lets in more air to both lean the mixture and raise the idle speed enough to keep the car running. They were used on automatic cars with A/C mostly where the idle speeds were fairly low to prevent transmission creep and the engine ran hotter because of the A/C. I believe they are also somewhat hard to come by these days.
Do they really work? I am not convinced of that but they look cute. They were sort of a Band-Aid fix anyway. Yes, cut the hose, remove a short section and put in the valve. | 
