I am not understanding why you have the ducts going through the doorway. Are you going to step over them?

If for example, you are exhausting 120 degree air through those ducts they are going to be HOT, ie burn yourself HOT.

an easier example would be to put the fan by the door, and then blow the air through the cards into an evase as it escapes the room. So shift the miners to be toward the back wall.

Remember that hot air rises, take advantage of that.