We study numerically the conjugate heat transfer between the walls of a parallel plate microchannel and ahomogeneous porous medium fully saturated with a liquid that is found in motion due to an external pressuregradient. The origin of this problem is caused by a uniform heat flux imposed at the external surfaces of the walls of themicrochannel that have a finite thermal conductivity. In this manner, the competition and heat transfer mechanismsbetween both regions characterized by the thermal resistances, conduct to a conjugate formulation that originates adimensionless conjugate parameter αc. This parameter measures the ratio of both thermal resistances, and, for largevalues of this parameter, the longitudinal heat conduction effects in the walls are very important and suffer significantdeviations when compared with the case with finite values for this parameter. The dimensionless governing equationsfor both regions are established with the corresponding boundary conditions, and the numerical results show that theaspect ratios of both regions, controlled through the dimensionless parameters ϵh and ϵ, play an important role indistinguishing the presence of the longitudinal heat conduction effects in the walls. For instance, if the ratios αc∕ϵ2h25 and αc∕ϵ2 1, the longitudinal effects of heat transfer are very important in the walls of the microchannel,whereas in the porous matrix there are effects of heat transfer in both directions, whereas if αc∕ϵ2h αc∕ϵ2 25 onlythe longitudinal conduction effects are significant for both regions.