This theoretical and numerical study investigates the natural convection flow within a fluid saturated porous medium enclosure subjected to intermittent heating from the side (hot wall). A theory for predicting the natural convection frequency of the flow wheel circulating inside the enclosure is developed from the general porous medium equations on a scaling basis. Physical insight indicates that heat flow resonance might occur when the input heat frequency matches the flow wheel circulating frequency. Numerical simulations confirm the existence of a preferred (resonance) input heat pulsating frequency. They also reveal that at the resonance frequency the fluid saturated porous medium system behaves as a dynamic thermal insulator in which the strong natural convection activity within the system, characterized by high amplitude heat flow oscillations, coexists with a damped oscillatory heat flux at the isothermal (cold) wall.