  We develop a variational theory of hot nuclear matter in neutron stars and
supernovae. It can also be used to study charged, hot nuclear matter which may
be produced in heavy-ion collisions. This theory is a generalization of the
variational theory of cold nuclear and neutron star matter based on realistic
models of nuclear forces and pair correlation operators. The present approach
uses microcanonical ensembles and the variational principle obeyed by the free
energy. In this paper we show that the correlated states of the microcanonical
ensemble at a given temperature $T$ and density $\rho$ can be orthonormalized
preserving their diagonal matrix elements of the Hamiltonian. This allows for
the minimization of the free energy without corrections from the
nonorthogonality of the correlated basis states, similar to that of the ground
state energy. Samples of the microcanonical ensemble can be used to study the
response, and the neutrino luminosities and opacities of hot matter. We present
methods to orthonormalize the correlated states that contribute to the response
of hot matter.
