CR and pump gas question

Does the aluminum really keep a "combustion chamber" cooler? Has anyone actually measured this? If you have iron and aluminum heads that make exactly the same horsepower and keep the water temperature the same in the jackets behind the combustion chamber, does the aluminum transfer heat better so you must have a better cooling system to maintain the water temperature?
Aluminum transfers heat better, so it stands to reason it could pull heat out of the combustion chamber to the water jackets better. Who knows if it's enough of an improvement to make any difference in chamber temps, but in theory it is some kind of improvement. It'd be like moving the coolant closer to the combustion chamber.