In your car, the little doors in the dash that direct air various places are vacuum actuated. As far as I can remember from the pictures in my Haynes, the servos are rubber things very much like the cruise control actuator you can see just behind your throttle cable drum under the hood. Sounds like the one that holds the door in the "floor" position has a leak that seals itself, or at least gets less severe, as it warms up.

These things are inside the dash and may be a real pain to get at.