  The interaction of light with a material's electronic system creates an
out-of-equilibrium (non-thermal) distribution of optically excited electrons.
Non-equilibrium dynamics relaxes this distribution on an ultrafast timescale to
a hot Fermi-Dirac distribution with a well-defined temperature. The advent of
time- and angle-resolved photoemission spectroscopy (TR-ARPES) experiments has
made it possible to track the decay of the temperature of the excited hot
electrons in selected states in the Brillouin zone, and to reveal their cooling
in unprecedented detail in a variety of emerging materials. It is, however, not
a straightforward task to determine the temperature with high accuracy. This is
mainly attributable to an a priori unknown position of the Fermi level and the
fact that the shape of the Fermi edge can be severely perturbed when the state
in question is crossing the Fermi energy. Here, we introduce a method that
circumvents these difficulties and accurately extracts both the temperature and
the position of the Fermi level for a hot carrier distribution by tracking the
occupation statistics of the carriers measured in a TR-ARPES experiment.
