A fan doesn’t chill the air. It cools you.
Moving air over your skin speeds up evaporation, and evaporating just one gram of sweat pulls about 2,400 joules of heat from your body.
But the room barely changes — a fan mostly reshuffles the same warm air.
So you’re cooling your skin, not the space. A fan left on in an empty room is really a tiny heater with a breeze.