  We compute the low-lying spectrum of the staggered Dirac operator above and
below the finite temperature phase transition in both quenched QCD and in
dynamical four flavor QCD. In both cases we find, in the high temperature
phase, a density with close to square root behavior, $\rho(\lambda) \sim
(\lambda-\lambda_0)^{1/2}$. In the quenched simulations we find, in addition, a
volume independent tail of small eigenvalues extending down to zero. In the
dynamical simulations we also find a tail, decreasing with decreasing mass, at
the small end of the spectrum. However, the tail falls off quite quickly and
does not seem to extend to zero at these couplings. We find that the
distribution of the smallest Dirac operator eigenvalues provides an efficient
observable for an accurate determination of the location of the chiral phase
transition, as first suggested by Jackson and Verbaarschot.
