This work examines the steady three-dimensional forced convective thermal boundary-layer flow of laminar and incompressible fluid in a porous medium. In this analysis, it is assumed that the solid phase and the fluid phase which is immersed in a porous medium are subjected to local thermal non-equilibrium conditions which essentially leads to one thermal boundary-layer equation for each phase. Suitable similarity transformations are introduced to reduce the boundary-layer equations into a system of nonlinear ordinary differential equations which are analyzed numerically using an implicit finite difference based Keller-box method. The numerical results are further confirmed by the asymptotic solution of the same system for the large three-dimensionality parameter, and the corresponding results agree well. Our results show that the thickness of the boundary layer is always thinner for all permeability parameters tested when compared to the non-porous case. Also, it is noticed that the temperature of the solid phase is found to be higher than the corresponding fluid phase for any set of parameters. There is a visible temperature difference in the two-phases when the microscopic inter-phase rate is quite large. The physical hydrodynamics to these parameters is studied in some detail.