A fan does not cool or heat the air in a room. Instead, it circulates the air, creating a breeze that can provide a cooling effect on your skin. This happens due to the process of evaporation.
When air blows across your skin, it increases the rate of evaporation of moisture from your body, which can make you feel cooler. The fan helps to disperse the heat from your body more efficiently by facilitating evaporation. However, it doesn't change the temperature of the air itself.
In fact, if the air in the room is already hot, a fan can sometimes make the room feel hotter because it can stir up and distribute the warm air. However, this is only a perception of increased warmth due to the movement of air; the actual temperature of the room remains the same.
To effectively lower the temperature in a room, you would need to use an air conditioning system or some other cooling mechanism that actively removes heat from the air.