The steady-state conduction of heat through the solid phase of a porous material consisting of an assembly of simple cubic packed uniform spheres at low liquid contents with heat conducted from one sphere to the next through annular liquid lenses around the points of contact, is analysed in terms of Legendre polynomials assuming the liquid bridges to behave as isothermal hemispheres around point sources and sinks. The conductance of a sphere is approximately the same when the surface area of the hemisphere is the same as that of the liquid lens assumed to be an isothermal disc for which numerical results of isotherms are compared with the analytical results. (c) 2006 Elsevier Ltd. All rights reserved.