We study the forced convective heat transfer from a uniform temperature cylinder placed perpendicular to an otherwise uniform fluid stream in a porous medium. Attention is focussed on how the absence of local thermal equilibrium between the solid and fluid phases affects the rate of heat transfer from the cylinder when the Peclet number is very large. It is found in all cases that the surface rate of heat transfer for the fluid is always greater than that of the solid matrix. Detailed numerical results are given for a wide range of parameter values, and these are supplemented by asymptotic analyses for both small and large values of the inter-phase heat transfer coefficient, H. When this coefficient is small the thermal field corresponding to the solid phase occupies a much greater region than does the thermal field of the fluid phase. (C) 2003 Editions scientifiques et medicales Elsevier SAS. All rights reserved.