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We also should correct these results, if to be used for analyzing lighting, for the different sensitivity of the eye at different wavelengths, to get an adjusted illumination value for the different spectral distributions. I can see this will not be a simple problem.
I guess I should have realized that. The total output is simply proportional to the square of the voltage. This assumes of course that resistance is constant, which in actuality it is not because it changes with temperature, and I think is less at lower temperature, so an adjustment for that would be required. According to https://en.wikipedia.org/wiki/Black-body_radiation, the power per unit area is σT4. But since power is proportional to the square of the voltage (assuming constant resistance), temperature varies as the square root of the voltage. As to how spectrum varies with temperature, Wein's displacement law says that the wavelength of maximum radiance varies inversely with temperature, which is to say, inversely with the square root of the voltage. However, this is not a complete answer because we require not just the wavelength of maximum emission, but the integral of the spectral curve within the visible band, to get the answer for the visible output; and the total power minus that would give the invisible output. This however is starting to become a complicated calculation.