  We reproduce the electronic properties of FeSe in the high-temperature phase
within an ab initio framework that includes screened Fock exchange and local
dynamical correlations. We robustly capture the experimental band structure, as
long as the system is in the Hund's metal phase. In particular, we account for
the shrinking of the Fermi pockets and the sinking below the Fermi level of the
hole pocket with $xy$ orbital character. This entails the elusive correct
estimate of the Sommerfeld coefficient, and supports the interpretation of
non-compensated Fermi pockets seen in ARPES in terms of surface electron
doping. More stringently, our modeling matches well the experimental interband
optical spectrum, and captures qualitatively the temperature dependence of the
thermoelectric power, extremely sensitive to the details of the bands around
the Fermi level.
