Hf-Al intermetallics are novel promising high-temperature structural materials for applications in automobile parts and aerospace industries, and presently attracting unprecedented research interest. It is obviously crucial to take into account thermodynamic properties such as thermal-expansion coefficients, specific heat at constant volume and constant pressure, and temperature-dependent bulk modules in the investigation of the properties of Hf-Al intermetallics as well as their applications. However, the reports for corresponding properties are very insufficient research and limited experimental data of them are hampering their large-scale application. Therefore, systematically calculating their thermophysical performance remains a necessary work. In this paper, we apply first-principles calculations within QHA to study the thermodynamic properties of Hf-Al intermetallics. The phonon-dispersion curves and phonon DOS have been discussed. Thermal expansions, temperature dependence of isothermal bulk modules and heat capacities at constant volume and constant pressure are presented. Phonon dispersion reveals that the contribution of Hf atoms is dominant in phonon frequency. In thermal expansion, we find HfAl3 > Hf2Al3 > Hf4Al3 > Hf2Al at high temperature while there exist little difference in specific heat between the structures. In addition, we consider the electronic contribution to the thermal properties, and our results show that the effects of thermal electronic excitations for Hf-Al intermetallics are remarkable.