The stability of the steady uniform flow of a power-law fluid down an inclined porous layer heated from below is investigated by means of a two-layer model. Under the long-wave approximation, the flow model is deduced starting from the continuity and momentum equations in the fluid film, the continuity and the generalized Darcy's law in the porous layer, and the energy balances in both the film and the porous layer. The associated boundary conditions account for the surface tension and the Beavers-Joseph velocity slip at the film bottom. A linear stability analysis of both two-dimensional and one-dimensional, i.e. depth-integrated, formulations is performed to define the neutral stability conditions, separately analyzing the S- and H-mode contributions. The influence of all the dimensionless governing parameters on the stability is discussed. Finally, the numerical solution of the depth-integrated model allows for an investigation of the nonlinear growth of H-mode unstable perturbations up to the formation of permanent waves and a discussion of the role of the magnitude of thermocapillary effects on the wave shape. Present results, taken collectively, indicate that, similarly to the isothermal case, the presence of a porous medium strongly modifies the stability bounds even in non-isothermal conditions, suggesting its potentiality as a passive control for the themocapillary instability for both H- and S-modes. Moreover, it is found that the shear-thinning behaviour leads to flows which are less stable but also less susceptible to thermocapillary effects.