The problem of unsteady free convection heat transfer from a one-dimensional (parallel) flow along an infinite vertical flat plate embedded in a thermally stratified fluid-saturated porous medium is considered. Flows are induced by a sudden change in the arbitrary temporal plate temperature. By a formal reduction of the corresponding boundary value problems to well-known Fourier heat conduction problems, analytical solutions of the Darcy and energy equations are obtained. Several special cases are discussed in detail.