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This paper presents a theoretical study using the Kármán-Pohlhausen method to describe the transient heat exchange between free convection in a boundary layer and a vertical flat plate embedded in a porous medium.  Unsteady behavior occurs after the generation of an impulsive heat flux step on the right-hand side of the plate.  Two cases are considered, depending on whether the plate has a finite thickness or no thickness.  The spatiotemporal evolution of the interface temperature is demonstrated.