  We present a grid of atmospheric models and synthetic spectral energy
distributions (SEDs) for late-type dwarfs and giants of solar and 1/3 solar
metallicity with many opacity sources computed in self-consistent Non-Local
Thermodynamic Equilibrium (NLTE), and compare them to the LTE grid of Short &
Hauschildt (2010) (Paper I). We describe, for the first time, how the NLTE
treatment affects the thermal equilibrium of the atmospheric structure (T(tau)
relation) and the SED as a finely sampled function of Teff, log g, and [A/H]
among solar metallicity and mildly metal poor red giants. We compare the
computed SEDs to the library of observed spectrophotometry described in Paper I
across the entire visible band, and in the blue and red regions of the spectrum
separately. We find that for the giants of both metallicities, the NLTE models
yield best fit Teff values that are ~30 to 90 K lower than those provided by
LTE models, while providing greater consistency between \log g values, and, for
Arcturus, Teff values, fitted separately to the blue and red spectral regions.
There is marginal evidence that NLTE models give more consistent best fit Teff
values between the red and blue bands for earlier spectral classes among the
solar metallicity GK giants than they do for the later classes, but no model
fits the blue band spectrum well for any class. For the two dwarf spectral
classes that we are able to study, the effect of NLTE on derived parameters is
less significant.
