  The chiral Gross-Neveu model is one of the most popular toy models for QCD.
In the past, it has been studied in detail in the large-N limit. In this paper
we study its small-N behavior at finite temperature in 2+1 dimensions. We show
that at small N the phase diagram of this model is {\it principally} different
from its behavior at $N\to \infty$. We show that for a small number $N$ of
fermions the model possesses two characteristic temperatures $T_{KT}$ and
$T^*$. That is, at small N, along with a quasiordered phase $0<T<T_{KT}$ the
system possesses a very large region of precursor fluctuations $T_{KT}<T<T^*$
which disappear only at a temperature $T^*$, substantially higher than the
temperature $T_{KT}$ of Kosterlitz-Thouless transition.
