  The linear-$\sigma$ model has been widely used to describe the chiral phase
transition. Numerically, the critical temperature $T_{c}$ of the chiral phase
transition is in agreement with other effective theories of QCD. However, in
the large-$N_{c}$ limit $T_{c}$ scales as $\sqrt{N_{c}}$ which is not in line
with the NJL model and with basic expectations of QCD, according to which
$T_{c}$ is --just as the deconfinement phase transition- $N_{c}$-independent.
This mismatch can be corrected by a phenomenologically motivated temperature
dependent parameter.
