A printer has a media transport with a rigid, air-transmissive platen. A movable air-transmissive flexible web overlays the platen. A suction device communicates with the platen to draw air through the web and through the platen such that a sheet of media carried on the web is biased toward the platen. A valve sheet overlays or underlies the platen, and includes a plurality of shut-off elements, each movable in response to temperature changes between a closed position in which the element contacts a portion of the platen to prevent air flow through that portion of the platen, and an open position, in which the element is spaced apart from the platen to admit air to the platen portion. The shut off elements may include resistive heaters and bimetallic strips, so that application of electricity generates heat to flex the strip to an open position.