  A recent Monte Carlo study of {\em quenched} QCD showed that the chiral
condensate is non-vanishing above $T_c$ in the phase where the average of the
Polyakov loop $P$ is complex. We show how this is related to the dependence of
the spectrum of the Dirac operator on the boundary conditions in Euclidean
time. We use a random matrix model to calculate the density of small
eigenvalues and the chiral condensate as a function of $\arg P$. The chiral
symmetry is restored in the $\arg P=2\pi/3$ phase at a higher $T$ than in the
$\arg P=0$ phase. In the phase $\arg P = \pi$ of the $SU(2)$ gauge theory the
chiral condensate stays nonzero for all~$T$.
