A semianalytic heat transfer model reproduces the temperature distributions measured inside the laser-heated diamond cell and constrains the temperature dependence of the thermal conductivity of dielectric mineral samples at high pressures and temperatures. Both axial and radial heat conduction determine the observed temperature distributions obtained from the TEM00 (Gaussian) and TEM01* laser modes. Measurements on the high-pressure perovskite-dominated assemblage of peridotite are consistent with the expected T-1 dependence of thermal conductivity at 45 GPa and temperatures between 1500 and 3800 K. ¿ 2001 American Geophysical Union