The relative importance of different heat transfer mechanisms is evaluated, and thermal conduction is found to dominate under most conditions achieved n the diamond anvil cell. The temperature distribution is calculated for metals and dielectrics heated by a laser. A comparison of calculated and measured temperature profiles across laser-heated perovskite samples indicates that the thermal conductivity is inversely proportional to temperature, as expected for dielectrics in which thermal conduction is due to phonon transport. A model is developed which relates laser power and sample temperature and permits the determination of thermal conductivity and absorption at high pressures and temperatures. The bias introduced by axial temperature gradients on measurements is negligible for experiments in which a metal foil is heated, but may lead to underestimating melting temperatures by 10% for dielectric samples at 4000 K.