We describe a flash-heating procedure designed to measure thermal diffusivity of materials at high pressure and temperature in diamond anvil cells. This technique involves time-resolved radiometry combined with a pulsed IR laser source. Results for MgO, NaCl, and KCl are presented (to P=32GPa and T=2600K). These measurements agree with previous studies at low pressure and high temperature and enable to test models for the combined P-T dependence of thermal conductivity. This technique can be extended to a broader range of pressures and can be used to address a variety of problems in geoscience, planetary sciences, and materials science.