Cool air from small opening and hot air from wide-open mouth

If you blow on your hand with your mouth open, your breath will be warm and if you do it with reducing the opening of your lips, your breath will be appreciably cooler. This is because expanding air is always cool and compressed air is always warm. A molecule picks up speed when it is hit by another molecule that approaches with a greater speed. But when a molecule collides with one that is receding, its rebound speed is reduced. The same idea applies to a region of air that is expanding: Molecules collide, on average, with more molecules that are receding than with molecules that are approaching. Therefore, in case of expanding air the speed of molecules decreases and thus cools the air. But in case of compressed condition, the molecule collide with more molecules that are approaching than with molecules that is receding. So, in case of compressed air the speed of molecules increases and thus warms the air.