Vent Needed For Door So Air Can Recirculate

I recently bought a house and it has a mudroom and in the mudroom is a furnace. We thought it was weird that the mudroom did not have a door because it led into the living room so I installed a door. Fast forward 3 months later and I was opposed to having a swamp cooler on the roof so I had a local contractor install a 4 ton 16.5 Seer Bryant AC Unit of which we are very happy with. At the end of installation the contractor mentioned to me that we had to leave the door open or install a vent in the top of the door when we used the AC so the air could be pulled back in and then DING the light went off and thats why the door had been gone. So I need to come up with some kind of a vent in the top of the door and I have looked around but have not found anything made for that purpose. Does anyone know if they make a vent for something like that? Something on the same principle of a cat door would do the trick but bigger. I would want it to look halfway decent on both sides if I could. I can post a photo of the door if that would help. We always had noticed that when we had the heat on that the furnace really had a big pull against that door but never really thought much about it. I guess it's a good thing we didnt use the heat much because the installer said that overtime it would cause damage with the entire system. Thank you for any help you can give me. tsfrance