The effects of Cr and W on high-temperature properties of Ni-based alloys are derived from first-principles calculations combined with a quasi-harmonic Debye model. The modeling procedure integrates all contributions from electronic excitations, magnetic fluctuations and lattice vibrations. The predicted lattice parameter and thermal expansion coefficient agree well with available reference values. The temperature dependence of elastic moduli for Ni-Cr alloys is described satisfactorily. Debye temperature has been calculated to show a strong volume dependence but a weak temperature dependence. A close relationship between the concentration dependence of elastic moduli and the volume dependence of Debye temperature, and thus the vibrational free energy, has been established. Besides, the softening of elastic moduli with increasing temperature is shown to be a result of thermal expansion which mainly comes from lattice vibrations. Therefore, lattice vibrations affect both temperature and concentration dependencies of elastic properties at elevated temperatures. With the help of Labusch-Nabarro model, solid solution hardening caused by Cr and W solutes in Ni has been analyzed. Moreover, the presence of solute atoms increases elastic anisotropy. The effects of Cr or W additions on the thermodynamic properties are found to be small compared to the effect of temperature.