The influence of heat transfer on the drying behaviour of capillary porous media saturated with water is studied. To overcome the limitations of continuum approaches, a pore network model based on statistical physics and invasion percolation is used. The presented non-isothermal model is the first of its kind to describe free evolution of temperatures in convective drying. Gas-side mass transfer is modelled by a discretised boundary layer. Model assumptions are purely conductive heat transfer in the network and negligible viscosity. Vapour condensation is partially modelled. Simulations are conducted on two-dimensional square lattice networks. Overall drying rates and corresponding evolution of phase distributions and temperature fields are presented for mono- and bi-modal pore structures. The influence of heat transfer on phase distributions and drying behaviour is discussed in comparison with isothermal simulations. (c) 2007 Elsevier Ltd. All rights reserved.