  We use quantum Monte Carlo methods in the framework of the interacting
nuclear shell model to calculate the statistical properties of nuclei at finite
temperature and/or excitation energies. With this approach we can carry out
realistic calculations in much larger configuration spaces than are possible by
conventional methods. A major application of the methods has been the
microscopic calculation of nuclear partition functions and level densities,
taking into account both correlations and shell effects. Our results for nuclei
in the mass region A ~ 50 - 70 are in remarkably good agreement with
experimental level densities without any adjustable parameters and are an
improvement over empirical formulas. We have recently extended the shell model
theory of level statistics to higher temperatures, including continuum effects.
We have also constructed simple statistical models to explain the dependence of
the microscopically calculated level densities on good quantum numbers such as
parity. Thermal signatures of pairing correlations are identified through
odd-even effects in the heat capacity.
