We study the thermal and chemical evolution during the Kelvin-Helmholtz pha
se of the birth of a neutron star, employing neutrino opacities that are co
nsistently calculated with the underlying equation of state (EOS). Expressi
ons for the diffusion coefficients appropriate for general relativistic neu
trino transport in the equilibrium diffusion approximation are derived. The
diffusion coefficients are evaluated using a held-theoretical finite-tempe
rature EOS that includes the possible-presence of hyperons. The variation o
f the diffusion coefficients is studied as a function of EOS and compositio
nal parameters. We present results from numerical simulations of proto-neut
ron star cooling for internal stellar properties as well as emitted neutrin
o energies and luminosities. We discuss the influence of the initial stella
r model, the total mass, the underlying EOS, and the addition of hyperons o
n the evolution of the proto-neutron star and on the expected signal in ter
restrial detectors. We find that the differences in predicted luminosities
and emitted neutrino energies do not depend much upon the details of the in
itial models or the underlying high-density EOS for early times (t < 10 s),
provided that opacities are calculated consistently with the EOS. The same
holds true for models that allow for the presence of hyperons, except when
the initial mass is significantly larger than the maximum mass for cold,ca
talyzed matter. For times larger than about 10 s, and prior to the occurren
ce of neutrino transparency, the neutrino luminosities decay exponentially
with a time constant that is sensitive to the high-density properties of ma
tter. We also find the average emitted neutrino energy increases during the
first 5 s of evolution and then decreases nearly linearly with time. In ge
neral, increasing the proto-neutron star mass increases the average energy
and the luminosity of neutrinos, as well as the overall evolutionary timesc
ale. The influence of hyperons or variations in the dense matter EOS is inc
reasingly important at later times. Metastable stars, those with hyperons t
hat are unstable to collapse upon deleptonization, have relatively long evo
lution times, which increase the nearer the mass is to the maximum mass sup
portable by a cold, deleptonized star.