We obtain the thermodynamic properties for a non-interacting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability P 0 between layers. The BEC critical temperature Tc coincides with the ideal gas BEC critical temperature T0 when P = 0 and rapidly goes to zero as P increases to infinity for any finite interlayer separation. The specific heat CV vs T for finite P and plane separation a exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than Tc which highlights the effects due to particle confinement. Then we discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of P . For T < Tc the crossover is revealed by the change in the slope of log CV (T ) and when T > Tc, it is evidenced by a broad minimum in CV (T ).