While it may seem counterintuitive, a fan does not actually make a room cooler by accelerating the average velocity of all molecules in the room. The cooling effect of a fan is due to a process called evaporative cooling and increased air circulation.
When a fan blows air across your skin, it speeds up the evaporation of moisture on your skin's surface. As the moisture evaporates, it absorbs heat energy from your body, making you feel cooler. This is why you feel a cooling sensation when a breeze from a fan hits you.
Additionally, a fan increases air circulation in a room, which helps in dissipating heat and reducing the temperature. The movement of air helps carry away the heat emitted by objects and bodies in the room, allowing for better heat exchange with the surroundings.
However, it's important to note that while a fan can create a cooling sensation and help with air circulation, it doesn't actually lower the temperature of the room. It only provides a perceived cooling effect on your body by facilitating heat transfer and increasing airflow. If the ambient temperature is high, using a fan alone may not be sufficient, and other cooling methods like air conditioning or ventilation may be needed to effectively lower the temperature.