This paper presented the investigation of the influence of the temperature−dependent screening effect on the Seebeck phonon drag coefficient Sg of a monolayer of bilayer graphene (BLG) and a BLG−BLG double layer placed in an air environment. For a system in an air environment, the two-dimensional electrons of the BLG was assumed to interact only with the intralayer deformation acoustic potential phonons in the BLG. After reviewing the results published by Kubakaddi and Bhargavi, “Enhancement of phonon-drag thermopower in bilayer graphene” in Phys. Rev. B 82, 155410 (2010), this paper expanded the mentioned-results to encompass the screening and double layers and found that the phonon drag coefficient in the BLG monolayer system was strongly reduced by the screening effect, even up to several orders of magnitude compared to the zero temperature screening function, as shown in some recent publications. When comparing the effect of electron screening in the second layer on electron-phonon interaction in the remaining layer, or on the intralayer screening function, the distance between the two layers was small. The screening effect of the second layer significantly reduced the magnitude of the phonon drag Seebeck coefficient Sg in the BLG-BLG double layer. The effect of temperature, layer spacing and particle density on Sg for symmetric and asymmetric systems with varying layer densities were also investigated.