  As part of a project to model the integrated spectra and colors of elliptical
galaxies through evolutionary synthesis, we have refined our synthetic spectrum
calculations of M giants. After critically assessing three effective
temperature scales for M giants, we adopted the relation of Dyck et al. (1996)
for our models. Using empirical spectra of field M giants as a guide, we then
calculated MARCS stellar atmosphere models and SSG synthetic spectra of these
cool stars, adjusting the band absorption oscillator strengths of the TiO bands
to better reproduce the observational data. The resulting synthetic spectra are
found to be in very good agreement with the K-band spectra of stars of the
appropriate spectral type taken from Kleinmann & Hall (1986) as well. Spectral
types estimated from the strengths of the TiO bands and the depth of the
bandhead of CO near 2.3 microns quantitatively confirm that the synthetic
spectra are good representations of those of field M giants. The broad-band
colors of the models match the field relations of K and early-M giants very
well; for late-M giants, differences between the field-star and synthetic
colors are probably caused by the omission of spectral lines of VO and water in
the spectrum synthesis calculations. Here, we present four grids of K-band
bolometric corrections and colors -- Johnson U-V and B-V; Cousins V-R and V-I;
Johnson-Glass V-K, J-K and H-K; and CIT/CTIO V-K, J-K, H-K and CO -- for models
having 3000 K < Teff < 4000 K and -0.5 < log g < 1.5. These grids, which have
[Fe/H] = +0.25, 0.0, -0.5 and -1.0, extend and supplement the color-temperature
relations of hotter stars presented in a companion paper (astro-ph/9911367).
