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In this work, we analyze the incidence of the plates? thickness on the Casimir force and radiative heat transfer for a configuration of parallel plates in a nonequilibrium scenario, relating to Lifshitz?s and Landauer?s formulas. From a first-principles canonical quantization scheme for the study of the matter-field interaction, we give closed-form expressions for the nonequilibrium Casimir force and the heat transfer between plates of thicknesses dL ,dR . We distinguish three different contributions to the Casimir force and the heat transfer in the general nonequilibrium situation: two associated with each of the plates and one to the initial state of the field. We analyze the dependence of the Casimir force and heat transfer with the plate thickness (setting dL = dR ≡ d), showing the scale at which each magnitude converges to the value of infinite thickness (d → +∞) and how to correctly reproduce the nonequilibrium Lifshitz?s formula. For the heat transfer, we show that Landauer?s formula does not apply to every case (where the three contributions are present), but it is correct for some specific situations. We also analyze the interplay of the different contributions for realistic experimental and nanotechnological conditions, showing the impact of the thickness in the measurements. For small thicknesses (compared to the separation distance), the plates act to decrease the background blackbody flux, while for large thicknesses the heat is given by the baths? contribution only. The combination of these behaviors allows for the possibility, on one hand, of having a tunable minimum in the heat transfer that is experimentally attainable and observable for metals and, on the other hand, of having vanishing heat flux in the gap when those difference are of opposite signs (thermal shielding). These features turns out to be relevant for nanotechnological applications.