The button between the up and down arrows is for the center vents (center and side) and prevents air from flowing to the floor and the defroster vents. This won't really make the air colder, but because it's all concentrated to one level may cool the car better and make it seem as if it's colder.
Are you sure you're not talking about the button under the down arrow - a button of circling arrows? Therie is the recirculation button and will make the AC colder because it restricts the introduction of outside air to the system.
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