Estimation of the thermal elastic effect is necessary for the calibration of the pressure and temperature conditions during laser-heated diamond anvil cell experiments, since above 800 K, the standard technique of using ruby fluorescence to measure pressure fails. Continuum calculations based upon the thermoelastic equations for an elastic medium were used to estimate the thermal pressure resulting from a radially symmetric temperature gradient in an elastic sphere with zero displacement on its surface. This calculation corresponds to the thermal pressure generated in a laser-heated diamond anvil cell sample that is compressed without a pressure medium. This solution must fall between circumstances where the sample is held at constant volume. It is shown here that the thermal pressure in an elastic medium with a Gaussian temperature gradient is approximately 40--60% of the thermodynamic value of the thermal pressure in a material raised to some constant temperature with the volume constrained to be constant. Even though the thermal pressure correction can be significant in terms of the total pressure that the sample experiences, these calculations indicate that the correction can be estimated to approximately 10%. ¿ American Geophysical Union 1990