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The rate of cooling is affected by the temperature difference between the warm substance (air in this case) and the substance that is gaining that heat. If they are close in temperature there will not be as fast am exchange of heat.

If the warm air and the cool air in the question are being cooled by transferring their heat to a substance at a set temperature, then the warmer air will cool faster, because it has a bigger temperature differential from the substance than does the cooler air.

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Q: Does hot air cool faster then cool air?
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