A new method to measure thermal diffusivity in samples at simultaneous high pressure and high temperature is presented. The sample is placed inside a cylindrical heater and subjected to a heater power that varies sinusoidally with time. The diffusion of the temperature variations into the sample is monitored using radiographic imaging of marker foils. This provides measurements of the phase lag and amplitude variation of the temperature cycle at a range of radii from the sample axis without the need for multiple thermocouples. The technique is tested using a NaCl sample at 4 GPa; the best-fit thermal diffusivity for NaCl at 4 GPa and 673 K is 2.4±0.5 × 10−6 m2/s.