The high temperatures typical of shock wave phenomena and planetary interiors require the use of anharmonic models accounting also for electronic effects in their description. By using a generalized form of the Gr¿neisen &ggr; function and its formulation in anharmonic lattice dynamics we find that at temperatures of a few thousand degrees Kelvin &ggr; is: 1) dependent on temperature as well as on volume; 2) different from the thermodynamical Gr¿neisen parameter &ggr;th =V&agr;KT/CV by a quantity of the same order of magnitude of &ggr;. This is not in contradiction with experimental data showing for many solids a quasi-independence of &ggr;th on temperature for T up to 1000¿C.