Unit cell volumes of the beta (β) and spinel (&ggr;) phases (Mg2SiO4) have been measured under simultaneous high pressure and high temperature using synchrotron X ray radiation, in a cubic anvil apparatus. With volume-temperature data at constant pressure, we determine the average volume thermal expansion coefficients of the β phase from 724 to 872 K at 7.6 GPa to be 2.28(¿0.45)¿10-5/K and of the &ggr; phase from 759 to 962 K at 9.8 GPa to be 1.71(¿0.14)¿10-5/K. Thermodynamic relations are used to constrain the temperature derivative of the isothermal bulk modulus (KT) from the high-pressure thermal expansion data: (ϵKT/∂T)P is found to be -2.7(¿0.5)¿10-2 GPa/K for the β phase and -2.8(¿0.3)¿10-2 GPa/K for the &ggr; phase. Unit cell volumes of the olivine (α) phase, back-transformed from the β and &ggr; phases at high temperatures, have been measured under pressure at temperatures above the Debye temperature; using thermal pressure equations, we find (ϵKT/∂T)P for the α phase to be -2.1(¿0.2)¿10-2 GPa/K. These new data on the temperature derivatives of the bulk modulus for the three phases are consistent with an upper mantle containing 60 to 65% olivine and the absence of a velocity signature for the β to &ggr; phase transition near 520 km depth. ¿ American Geophysical Union 1993