  Three-quark potentials are studied in great details in the three-dimensional
$SU(3)$ pure gauge theory at finite temperature, for the cases of static
sources in the fundamental and adjoint representations. For this purpose, the
corresponding Polyakov loop model in its simplest version is adopted. The
potentials in question, as well as the conventional quark--anti-quark
potentials, are calculated numerically both in the confinement and
deconfinement phases. Results are compared to available analytical predictions
at strong coupling and in the limit of large number of colors $N$. The
three-quark potential is tested against the expected $\Delta$ and $Y$ laws and
the $3q$ string tension entering these laws is compared to the conventional
$q\bar{q}$ string tension. As a byproduct of this investigation, essential
features of the critical behaviour across the deconfinement transition are
elucidated.
