Abstract: Roller grate material bed conveying and heat transfer apparatus which provides plural bed depths has cylindrical horizontal rollers driven in the same direction with gas passage apertures in the rollers and filler members in the nip between adjacent rollers. Means are provided to pass heat transfer gas streams through the bed as the rollers urge the material particles in a direction transverse to the roller axes and continually tumble the particles so that all surfaces thereof are exposed to the gas streams. A first plurality of rollers are positioned in a first generally horizontal plane to receive the material fed to the apparatus, and a second plurality of rollers downstream from the first rollers are at elevations lower than the first horizontal plane and preferably are driven at slower speed than the first rollers to thereby increase the material bed depth downstream from the first horizontal plane as the material particles are hardened by heat and can withstand greater bed depth without crushing.