If you're confidant that the air leaving the house through the open window is warmer than the outside air that will come back in to replace it, I suppose it's OK to leave the window open. But I think a better solution would be to shut the AC off and use a window fan to circulate the cool outside air through the house. A window fan will be quieter and more energy efficient than an AC, and probably faster at cooling as well.
Which direction the fan faces doesn't matter a ton as long as you're moving the air around, but if you think about the goal of getting the hot air out of the house and the cool air in, here are some ways to think about it:
- If the wind is generating any air movement through a window, use the fan in the same direction. No point in fighting nature.
- If you have a single floor, put one fan blowing in and one fan blowing out, at opposite sides of the house.
- If you have several floors, put a fan on the lower floor blowing in, and a fan on the upper floor blowing out.
- If you still can't decide, point the fan facing out so that the waste heat generated by the fan isn't pushed into the room.