The differential formulation employing a self-consistent concept is extended to study the directional response of overall thermal conductivity in a porous medium containing anisometric pores. The anisometric pores distribute in a special direction relative to the incoming heat flux vector, rendering an anisotropic overall thermal conductivity tenser when discharging the heat flew in the porous medium. Cylindrical cavities with insulated surfaces are exemplified in the numerical example, demonstrating the directional response. Effects of the preferential orientation and the aspect ratio of the cylindrical cavities on the anisotropy of the overall thermal conductivity tenser are studied.