The productivity of Fischer-Tropsch reactors is determined by the efficiency of heat and mass transfer processes inside the catalyst granules. To reduce the diffusion resistance the granules base is made from ceramic highly porous material. The porous structure of the granules causes a discrete arrangement of cobalt metallic microparticles whose size can reach tens of microns. Cobalt particles are the active centres on which the synthesis reactions are realized. The distance between these active centres significantly exceeds their characteristic size and the homogeneous model for heat and mass transfer is incorrect. In our paper a mathematical model of heat and mass transfer processes in a porous spherical granule with localised active centres is proposed. The heat of the exothermic synthesis reaction is removed from the surface of the granule by heat transfer into the synthesis gas stream washing the granule. The components of the synthesis gas enter to the granule surface as a result of mass transfer. On the basis of the mean-field approach the values of the temperature and concentration of the synthesis gas components at the active centres inside the granule were determined. In the reactor tube, where the catalyst granules are placed, there is a critical temperature. The excess of the critical temperature leads to a thermal explosion, i.e. a substantial overheating of the active centres. In this case, the surface of the catalyst granule is superheated slightly. The principal difference between the homogeneous and heterogeneous models in catalytic reactions is discussed. We analysed influence of the temperature inside the reactor tube, size of the granule, and coefficient of thermal conductivity on the thermal stability of the granule. (C) 2018 Elsevier Ltd. All rights reserved.