I have something similar in my house for my full tower.
Didn't need a vent over the stairs, so I went to HD, bought ac duct, ran it to the computer room, punched a hole in the ceiling, and ran the duct behind the computer desk to the front of the computer. My computer desk is huge, so you barely see the duct running down the wall.
In the winter when the heat is running, I point the duct to the door and the air goes out the computer room. If it's too hot, I just open the window and let the cold air in. In the summer, having two vents blowing cold air into the room really helps.