Using recent and accurate experimental information on various thermodynamic quantities up to the melting temperature Tf of molybdenum and tungsten, we make a detailed study of some of their high- temperature properties. In particular, we consider the entropy, reduced to a fixed crystal volume, and interpret the result in terms of an electronic part and a temperature-dependent entropy Debye tempera- ture. The analysis reveals large explicit anharmonic effects. When plotted versus the reduced tempera- ture T/Tf, various quantities of Mo and W related to anharmonicity show a striking similarity. For in- stance, the heat capacity Cz is the same for Mo and W, to better than 1%, for T/Tf ) 0.2. We also make a detailed study of the temperature dependence of the Gruneisen parameter at constant pressure and at constant volume. below 400 K. This paper focuses on transition metals, up to their melting temperature. We choose to consider molybdenum and tungsten, since their extreme melting temperatures (Tf =2896 K for Mo and 3695 K for W) cause features we wish to study to be pronounced. The shape of the electron density of states of the solid (bcc) phase, with a deep and broad minimum around the Fermi level, stabilizes the solid relative to the liquid and pushes up the melting temperature. One may thus view bcc Mo and W at high temperatures as overheated solids, which make them favorable for a study of high-order anharmonic eA'ects in the lattice vibrations. In a previous paper we gave a qualitative account of many exceptional thermodynamic properties of tungsten, relying on the shape of the electron density of states. Those results remain valid, but we shall here reconsider W and extend the discussion to properties at fixed volume, using more recent experimental data. The analysis of molybdenum is presented in detail. That in- cludes a critical evaluation of the heat capacity, the enthalpy, and the pressure and temperature dependence of the molar volume, from which we calculate the entro- py S(T, Vo) at fixed volume Vo. The contribution to S from conduction electrons is evaluated from the electron band structure. The remainder in S, of vibrational origin, gives information about the low- and higher-order anhar- monic corrections. We shall also study in detail the tem- perature dependence of the Gruneisen parameter and comment on striking similarities between molybdenum and tungsten when some of their properties are compared at equal reduced temperatures T/T&.