  We apply a previously developed asymptotic model (J. Fluid. Mech. 915, A133
(2021)) to study instabilities of free surface films of nanometric thickness on
thermally conductive substrates in two and three spatial dimensions. While the
specific focus is on metal films exposed to laser heating, the model itself
applies to any setup involving films on the nanoscale whose material parameters
are temperature-dependent. For the particular case of metal films heated from
above, an important aspect is that the considered heating is volumetric, since
the absorption length of the applied laser pulse is comparable to the film
thickness. In such a setup, absorption of thermal energy and film evolution are
closely correlated and must be considered self-consistently. The asymptotic
model allows for a significant simplification, which is crucial from both
modeling and computational points of view, since it allows for asymptotically
correct averaging of the temperature over the film thickness. We find that the
properties of the thermally conductive substrate -- in particular its thickness
and rate of heat loss -- play a critical role in controlling the film
temperature and dynamics. The film evolution is simulated using efficient
GPU-based simulations which, when combined with the developed asymptotic model,
allow for fully nonlinear time-dependent simulations in large three-dimensional
computational domains. In addition to uncovering the role of the substrate and
its properties in determining the film evolution, one important finding is
that, at least for the considered range of material parameters, strong in-plane
thermal diffusion in the film results in negligible spatial variations of
temperature, and the film evolution is predominantly influenced by temporal
variation of film viscosity and surface tension (dictated by average film
temperature), as well as thermal conductivity of the substrate.
