Applying the variational principle of BOGOLIUBOV to calculate the free energy of a quantum system one does not get, automatically, physical meaningful results for entropy and specific heat. By using the temperature in the ansatz for the statistical operator as a variational parameter it is proved, that at any rate, the approximation expression for free energy has the properties of a thermodynamic function, that means, it leads to positive values for specific heat and entropy, and to a GIBBS—HELMHOLTZ equation for entropy and free energy.