Promising
applications in photonics are driven by the ability to
fabricate crystal-quality metal thin films of controlled thickness
down to a few nanometers. In particular, these materials exhibit a
highly nonlinear response to optical fields owing to the induced ultrafast
electron dynamics, which is however poorly understood on such mesoscopic
length scales. Here, we reveal a new mechanism that controls the nonlinear
optical response of thin metallic films, dominated by ultrafast electronic
heat transport when the thickness is sufficiently small. By experimentally
and theoretically studying electronic transport in such materials,
we explain the observed temporal evolution of photoluminescence in
two-pulse correlation measurements that we report for crystalline
gold flakes. Incorporating a first-principles description of the electronic
band structure, we model electronic transport and find that ultrafast
thermal dynamics plays a pivotal role in determining the strength
and time-dependent characteristics of the nonlinear photoluminescence
signal, which is largely influenced by the distribution of hot electrons
and holes, subject to diffusion across the film as well as relaxation
to lattice modes. Our findings introduce conceptually novel elements
ruling the nonlinear optical response of nanoscale materials, while
suggesting additional ways to control and leverage hot carrier distributions
in metallic films.