Abstract: An attached tube cooler for a rotary kiln for cooling solid particulate material discharged from the kiln. The cooler includes a plurality of cylindrical vessels attached to and circumferentially spaced around the discharge end of the kiln for rotation therewith. Each cooler tube has an inlet for solid particulate material communicating with the outlet of the kiln, an outlet for cooled solid particulate material, an inlet for cooling gas and an outlet for gas which communicates with the kiln so that gas heated in the cooler tube can be supplied as combustion air to the kiln. Heat exchange fins are mounted inside the cooling tube at an angle such that the trailing surface of the fins in the direction of tube rotation forms an acute angle with the side wall of the cooler tube. A helical conveyor having a central opening therethrough advances material through the cooler tube.