We analyzed the role of the inclusion of anti-dots on the vortex state and some calorimetric properties of a mesoscopic superconducting square immersed in an external applied magnetic field. We calculated the magnetization, entropy, Gibbs free energy, density of Cooper pairs and specific heat for this system in a zero field cooling process, solving the time-dependent Ginzburg–Landau equations. We found that the critical temperature is non-dependent on the number of anti-dots and dependent slightly on the size of the defects. Oscillations in the entropy and specific heat are found due the temperature dependence of the superconducting characteristics length.