  Using time- and angle-resolved photoemission spectroscopy, we study the
response of metallic single layer TaS$_2$ in the 1H structural modification to
the generation of excited carriers by a femtosecond laser pulse. A complex
interplay of band structure modifications and electronic temperature increase
is observed and analyzed by direct fits of model spectral functions to the
two-dimensional (energy and $k$-dependent) photoemission data. Upon excitation,
the partially occupied valence band is found to shift to higher binding
energies by up to 150 meV, accompanied by electronic temperatures exceeding
3000~K. These observations are explained by a combination of
temperature-induced shifts of the chemical potential, as well as
temperature-induced changes in static screening. Both contributions are
evaluated in a semi-empirical tight-binding model. The shift resulting from a
change in the chemical potential is found to be dominant.
