We have presented an analysis of the volume expansion data for periclase (MgO), lime (CaO), corundum (Al2O3) and spinel (MgAl2O4) determined experimentally by Fiquet et al (1999) from 300K up to 3000K. The thermal equation of state due to Suzuki et al (1979) and Shanker et al (1997) are used to study the relationships between thermal pressure and volume expansion for the entire range of temperatures starting from room temperature up to the melting temperatures of the solids under study. Comparison of the results obtained in the present study with the corresponding experimental data reveal that the thermal pressure changes with temperature almost linearly up to quite high temperatures. At extremely high temperatures close to the melting temperatures thermal pressure deviates significantly from linearity. This prediction is consistent with other recent investigations. A quantitative analysis based on the theory of anharmonic effects has been presented to account for the nonlinear variation of the thermal pressure at high temperatures.