Applying external heating reduces temperature gradients in the laser-heated diamond cell by roughly a factor of two as the external temperature is raised by 300 K. A heat conduction model is presented which can account for most of the reduction. In addition, the temperature distribution measured in a (Mg0.86Fe0.14)SiO3 perovskite sample at 56 GPa is compatible the expected inverse temperature-dependence of thermal conductivity. ¿ American Geophysical Union 1996