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In this work, we have calculated the thermal properties of H2 and O2 diatomic molecules with multi parameter exponential type potential within the framework of the statistical mechanics. In this regard, using the improved energy spectrum, we have determined the vibrational partition function obtained recently via the path integral formalism. Based on obtained partition function, we find thermodynamic properties of diatomic molecules such as Gibbs free energy, enthalpy and specific heat in constant pressure by the Poisson summation formalism. Also, we have validated our results with experimental data and our results show that there is a good agreement between them. Finally, the average absolute deviations of the calculated data from the experimental data are obtained. [ABSTRACT FROM AUTHOR]