A multi-sectional through-flow apparatus, proposed by Kostromskoij et al. [L.E. Gnevanova, G.A. Kostromskoi, S.S. Skachkova, 1985. Hydrodynamics of multisectional fluidized bed cooler of sphere pellets. In: Calculations and Investigations of Concentrating Equipment, VNIIMETMASH, Moscow, pp. 33-39 (in Russian).], is described. In this apparatus, stable fluidization of particles with deep and uniform cooling or heating is ensured by use of an inclined gas distributor of low pressure drop. The pattern of particle circulation was investigated. Formulae for calculating the fluidization velocity at the start of particle movement and for computing the pressure drop and rate of particle cooling by the gas were derived. Characteristics of operating commercial apparatus are given.