  We investigate a temperature-based model, called extended two-temperature
model (eTTM), that describes the electronic non-equilibrium and its effect on
energy dissipation in metals after ultrashort laser excitation. We derive and
discuss improvements in comparison to published versions of this model [E.
Carpene, Phys. Rev. B 2006, 74, 024301; G. Tsibidis, Appl. Phys. A 2018, 124,
311]. The comparison of the results of the eTTM with results of the well-known
two-temperature model (TTM) shows a delayed increase of the electronic
temperature when being calculated with the eTTM. We find a good agreement in
the non-equilibrium energy distribution after absorption of photons with
results from a kinetic description using a Boltzmann collision term. The model
provides a convenient tool for fast calculation of features of the
non-equilibrium electrons. As an example we inspect the dynamics of high-energy
electrons observable in photo-electron spectroscopy and demonstrate the
advantage of the eTTM over the conventional two-temperature model.
