A model has been developed to simulate combustion and heat transfer in a porous matrix combustor-heater. The system consists of a packed bed in which a premixed natural gas-air mixture combusts. Radiative and convective heat transfer occurs from the flame zone to a fluid flowing through a bank of tubes embedded in the packed bed. Radiative heat transfer in the bed is modelled as a diffusion process, and the flow and temperature fields of the gas and solid matrix in the bed are calculated by solving the mass, momentum, energy and species conservation equations accounting for variations of thermophysical properties with temperature. Allowance is made for a finite heat transfer rate between the gas and the solid matrix, i.e., the temperatures of the gas and the solid matrix are not equal locally. The effects of particle diameter, excess air, and firing rate are examined and their influences on the thermal performance of the porous matrix combustor-heater are discussed. The sensitivity of the model to the volumetric heat transfer coefficient is also investigated and discussed. The numerically obtained results are compared with available experimental data for a similar system, and the predictions are found to agree with test data within the experimental uncertainty. The difference between the predictions of this model and a previous model based on the assumption of thermal equilibrium between the gas and solid matrix increases as the bed particle diameter increases