Numerical and analytical results of the investigation of the thermodynamic properties of a quasi-2D electron gas are presented. The density of states, the temperature derivative of the chemical potential, and the heat capacity of the gas at the resonance points and away from it are analyzed. It is shown that, in the dependence of the heat capacity on the chemical potential, there are additional steps at the resonance points. The width of the additional steps increases with temperature. With the increase in temperature, when the main steps are practically blurred, there are still visible marks from the additional steps.