  For a "reference day" of minimal solar activity between cycles 23 and 24 we
compute the brightness temperature from solar spectral irradiance for each
wavelength. We consider small variations of irradiance and temperature about
the reference day values, and derive linear and quadratic analytic temperature
approximations by Taylor expansion about the reference values. To determine
approximation accuracy we compare to exact brightness temperatures computed for
each day. We find that the linear analytic approximation overestimates, while
the quadratic underestimates the exact result. Using R software, we find
statistical fit models with minimum root-mean-square-error. We show that the
quadratic statistical fit models give the smallest root-mean-square-error,
giving results very near the exact.
