what kinda windows let you open them from the top and the bottom
This is why you might consider ducting, and inline fans. you can get a piece at home depot that turns a 6" round into a flat 2" tall rectangle that will fit right under your open window. Get two of them right next to each other, one for intake, and one for exhaust. Then cover the rest of the open part of the window with some sort of insulation, and you never have to open it, and your plants get fresh air.
Its not just about cooling the lights. LED's shouldn't need too much of that. Its about oxygen saturation. If the plants go too long without fresh air, they will suck up all the co2 in the inside air, and essentially get oxygen poisoning, which is not good. Just leaving the door open should be enough to stop that from happening, but I would suggest using the window in the room with the plants for fresh air, because your plants will be much more healthy. This way you can close the door to the room as well, in case its colder in there than the rest of the house. That way your not pumping all your house heat outside., you could get 2 used 6" fans for $100 if you tried. even 2 4" fans would be fine for an led setup, and cheaper yet.