The box probably has blend door in it that mixes air from the heater core and air conditioner evaporator. It is possible the force of the wind on the door is enough to move it to the center or neutral position half way between the two sources as the parts are likely old and loose. You should be able to put a bit of squish on the inner cable if you can find a cable housing retaining clamp or can add on. Clamp a little tight on the housing or put a shim in it to squeeze more, and it usually will tighten up the cable so it stays put.
