Diffusion of heat in metals is a fundamental process which is crucial for a variety of applications of metal nanostructures. Surprisingly, however, {em ultrafast} heat diffusion received only limited attention so far. Here, we show that heat diffusion can be made faster than $e-ph$ energy transfer rate, in which case, it dominates the spatio-temporal dynamics of the temperature. This enables the metals to overcome the conventional limitations of the nonlinear optical response of materials - it can be simultaneously fast and strong. As a specific example, we identify the underlying (femtosecond and few picosecond) time scales responsible for the generation and erasure of optically-induced transient Bragg gratings in thin metal films. Further, we show that heat diffusion gives rise to a significant nonlocal thermo-optic nonlinearity - it affects also the nonlinear optical response such that the overall change of the permittivity (hence, reflectivity of the transient grating) has a significant dependence also on the illumination period rather than only on the illumination intensity.
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