Apparatus for the heat treatment of fine material comprises a multi-stage cyclone preheater, a rotary kiln and a calciner supplied with tertiary air from a cooler for precalcination of the preheated fine material. The tertiary air pipe is narrowed at the point where it joins into the calciner. In this way an intensification of the mixing together of material, fuel and gas is achieved as well as an improved combustion, particularly fuels which are slow to react.