In this paper, we have investigated the specific heat of a quantum dot superlattice system in the presence of a magnetic field parallel to the superlattice axis and confined in a lateral parabolic quantum well. We took the effect of the Rashba spin-orbit interaction and Zeeman term on the specific heat into account. We have calculated the energy spectrum of the electron in the quantum dot superlattice system. Moreover, we have calculated the specific heat dependence on the magnetic field and temperature of a quantum dot superlattice system.