  Using the graded eigenvalue method and a recently computed extension of the
Itzykson-Zuber integral to complex matrices, we compute the $k$-point spectral
correlation functions of the Dirac operator in a chiral random matrix model
with a deterministic diagonal matrix added. We obtain results both on the scale
of the mean level spacing and on the microscopic scale. We find that the
microscopic spectral correlations have the same functional form as at zero
temperature, provided that the microscopic variables are rescaled by the
temperature-dependent chiral condensate.
