A self-compensating constant-tension drive system for a belt conveyor used in a cryogenic freezing tunnel or other elongated thermal processing apparatus, comprising a hydraulic motor driving the drive pulley of the conveyor, a hydraulic pump driven by the tensioning pulley, and a pressure relief valve connected to the outlet of the pump to inhibit flow from the pump and thus inhibit rotation of the pump and tensioning pulley until a predetermined tension is established in the upper run of the belt; the belt is longer than the inter-pulley spacing to allow for substantial thermal expansion and contraction, and the excess belt length is stored in a catenary sag adjacent the drive pulley.