Okay so I’m hot. I’m sitting here with a folded up bit of card fanning myself and it’s cooling my skin nicely. But it has no long term effect and eventually my arm gets tired. It occurs to me that the constant movement of my arm is increasing my blood circulation and keeping me hot. So how effective is fanning? Is it a false economy?
If it feels cooler to do it, then yes it is. Your arm will heat up due to the exercise of its muscles, but the cooling effect of increased evaporation of sweat from a large area of skin should more than counteract that. It’s a similar consideration for having an electric fan in the room; the motor puts out some heat so the overall heat in the room goes up, but you are cooler due to the sweat effect.
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In general, only if ambient temperature is less than body temperature.
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However if you are sweating or otherwise wet, the increase in evaporation will increase cooling. Try rolling a towel or paper towel into a cylinder, wetting it, and putting it around your neck.
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If you are next to some sort of cool spot (fridge, bowl of ice, whatever), air movement will transport the cool air to you faster than just letting things be.