The issue of local thermal equilibrium between a solid porous matrix and a saturating (stagnant) fluid under unidirectional steady heat diffusion is considered focusing on the effect of exterior-boundary thermal conditions. We demonstrate that in the case of exterior boundaries with uniform heat Aux, i.e., when the heat per unit of phase area flowing through each phase is equal. thermal equilibrium will ensue only when the phases have the same thermal conductivity. When the phases are in thermal equilibrium at the exterior boundaries, then they will be in thermal equilibrium throughout the entire domain independently of the properties of each phase. In this case, the ratio of the heat flowing through each phase will be uniform within the layer and proportional to the thermal conductivity phase-ratio. With uniform heat flux at one end and thermal equilibrium at the other end of the domain, four independent criteria lead to thermal equilibrium. For a small fluid-to-solid volumetric heat transfer coefficient the medium reaches a state of maximum thermal nonequilibrium. A criterion for estimating the thermal equilibrium status within the layer is also derived. This criterion is important for the experimental determination of the effective thermal conductivity of a saturated porous layer.