The fired or sintered material is discharged into a trough between an inclined traveling hearth and a fixed wall until the trough is substantially filled with the material. A gaseous cooling medium is conducted continuously through the fixed wall into the material in the trough, and material is carried on the traveling hearth in an upwardly inclined direction out of the trough and then horizontally away from the trough, the speed at which material is carried on the traveling hearth and the rate at which hot material is discharged into the trough being such that the depth of the horizontally traveling material on the traveling hearth is substantially less than the depth of the material in the trough.