The thermal stability of cubic metals in both solid and solid-liquid melt phases is discussed in terms of anharmonic effects such as due to Gruneisen parametery. A thermodynamic equation relating γ and a stability determinantD for solid metals is derived, followed by a presentation of the temperature dependence ofD. An analysis of the estimatedD values shows the stability determinant to be a direct function of temperature for the solid metals, but decreases on melting. The magnetic changei.e. second-order phase transformation of a solid metal is theoretically considered to be associated with a minimum of the Gruneisen parameter and a maximum in the intensity of energy fluctuation. Some thermodynamic equations involving γ and heat capacity are derived which relate the properties of a metal at the two-phase solid-liquid melt regime to its properties in the solid region. An analysis of the estimated data shows a very small increase in γ from the solid bulk to the melt phase. However, the heat capacity data which are expected to be fairly similar for all metals at fusion, are estimated to be different for metals in the melt regime and are higher compared to the corresponding values in the solid region.