By "hand fan" I'm referring to the kind of fan which is human-powered (link to Wikipedia article).
The problem is that by the second law of thermodynamics, the heat generated by operating the fan ought to outweigh the cooling that's experienced. With electric fans there's no problem since the agent doing the work isn't the person, but with hand fans, the operator is effectively heating up one part of his body to cool a different part. We expect that the heat generated is greater than the heat removed, which implies that hand fans are actually counterproductive. If we locked a person in a room with a hand fan, the room should heat up faster if he uses the fan than if he doesn't!
How is this apparent violation of the second law explained?