The second and fourth moments of the phonon spectrum are calculated for the refractory metals Mo and W, with the effective interaction potentials fitted to the results of the local density approximation calculations. The temperature dependence of the Debye temperature is discussed. It is shown that the obtained potentials give a good agreement of cohesive properties with the data calculated from the universal function of Rose er al. [Phys. Rev. B 29, 2963 (1984)]. The Gibbs-Bogoliubov inequality and the variational procedure of Ross [J. Chem. Phys. 71, 1567 (1979)] are used for the calculations of the temperature dependence of free energy in liquid tungsten. The calculated thermodynamic functions of solid and liquid phases are employed to determine the melting temperature.