Thermally driven flow in a thin, inclined, rectangular cavity filled with a non-Newtonian fluid saturated porous medium is considered. A constant heat flux is applied for heating and cooling the two side walls of the layer while the other two walls are insulated. The problem is solved on the basis of a modified Darcy equation. In the limit of a thin layer, using a parallel flow approximation and an integral form of the energy equation, the governing equations are reduced to one ordinary differential equation. Solutions for the flow and temperature fields, and the Nusselt number are obtained for various Rayleigh numbers, R, the inclination angle of the cavity, phi, and the power-law index, n. A numerical study of the same problem is also conducted by solving the complete system of governing equations. A good agreement is found between the parallel flow analysis and the numerical simulation.