A model of heat transfer in an infiltrated granular bed, which allows for most important special features of the process, viz., anisotropy of thermal properties and nonuniform distribution of the porosity and gas (liquid) velocity cover the cross section, has been formulated. The concepts of the filtration boundary layer and viscous sublayer have been introduced and identified. Temperature fields and values of the coefficient of heat exchange between the bed and the wall of the tube bounding it have been calculated. The latter are generalized in the form of the dimensionless correlation which is compared with the available experimental data. It is shown that at Re-infinity <= 2000 the developed model describes the process of heat transfer in the granular bed well. (C) 2006 Published by Elsevier Ltd.