Abstract: A planetary cooler system is disclosed for cooling hot cement clinker exiting from a rotary kiln having a plurality of cooler tubes mounted in planetary fashion there-about and being adapted to receive material from the rotary kiln into their inlet end portions. A material outlet casing communicates with the planetary cooler tubes and is adapted to receive at least partially cooled hot material from the outlet portion of each cooler tube when its rotational position is at or near its uppermost position. The outlet casing defines two shafts joined at their upper ends and configured and adapted to receive the partially cooled cement clinker from the tubes for passage down through the shafts to cause the outlet casing to act as a shaft cooler, while at least one ventilating device blows or draws cooling air through the casing to provide further cooling of the clinker preferably countercurrently to its passage therethrough. The invention also relates to a rotary kiln plant incorporating the cooler system.