It has been demonstrated that an all-optical interferometer can be used to measure directly the thermal diffusivity of nonlinear materials by measuring optical path differences only. A lithium niobate crystal was inserted into an interferometer and heated by its absorption of an input pulse from a focused CO2 laser. As the heat diffuses outward in the crystal, the refractive index increases and the crystal expands. The resulting optical path change can be monitored interferometrically in real time, and from fringe data the thermal diffusivity is determined. A Gaussian model for the temperature distribution was derived and verified empirically. The method is quite general and should work for a variety of materials given the proper laser probe and (heat) pump wavelengths. It avoids the need to measure temperature distributions, powers, and critical crystal parameters, dimensions, and angles.