The door for the middle chamber - i. e., the door which gave access to the mid-most “set of chambers.” The chambers on the ground-floor were possibly reached each by their own door in the outer wall of the lean-to. The middle and upper floors were reached by a single door in the right or south wall, from which a winding staircase ascended to the second tier, while another ascended from the second to the third. The door to the stairs was in the outer wall of the building, not in the wall between the chambers and the temple. That would have desecrated the temple far more than the insertion of beams.
Related Commentaries of 1 Kings 6:8
1 Kings 6:8
8 The door for the middle chamber was in the right sideb of the house: and they went up with winding stairs into the middle chamber, and out of the middle into the third.