  In this paper we study a random matrix model with the chiral and flavor
structure of the QCD Dirac operator and a temperature dependence given by the
lowest Matsubara frequency. Using the supersymmetric method for random matrix
theory, we obtain an exact, analytic expression for the average spectral
density. In the large-n limit, the spectral density can be obtained from the
solution to a cubic equation. This spectral density is non-zero in the vicinity
of eigenvalue zero only for temperatures below the critical temperature of this
model. Our main result is the demonstration that the microscopic limit of the
spectral density is independent of temperature up to the critical temperature.
This is due to a number of `miraculous' cancellations. This result provides
strong support for the conjecture that the microscopic spectral density is
universal. In our derivation, we emphasize the symmetries of the partition
function and show that this universal behavior is closely related to the
existence of an invariant saddle-point manifold.
