An analysis has been made for the pulsating flow of gas and the accompanying heat transfer within a regenerator made from mesh screens. A flow model is developed taking the mesh as a non-Darcy, thermally non-equilibrium porous medium. A harmonic analysis technique is used for solving the fully developed but unsteady gas flow in the regenerator. Based on the flow solution thus obtained, slowly evolving axisymmetric unsteady thermal fields are solved numerically over a wide range or frequencies by making use of the finite volume method. Presentation is made of the friction factor and regenerator effectiveness. Effects of Reynolds number and frequency on the temperature profile and the transient behavior of tile system ore discussed. The importance of a thermal time constant of the system and length-to-radius ratio of the regenerator demonstrated.