In the embodiment described in the specification, a hot melt ink image on a substrate is treated in a continuous manner by moving it along a platen having a heating zone to melt drops of hot melt ink and cause them to spread on the substrate. The platen has a flat central portion and curved portions at each end with curvatures sufficient to prevent formation of cockle. At the output end of the heating zone, the substrate is moved continuously into a quenching zone where a cooling platen cools the substrate by thermal contact at a rapid rate to prevent crystallization or frosting of the hot melt ink image. After the quenching zone, the substrate is moved along a surface having a reverse curvature with respect to the curved portions of the heating platen to eliminate residual curvature of the substrate resulting from the curved portions of the heating platen.