To achieve the level of accuracy you're alluding to requires curve fitting the spectral output to the ideal blackbody, which requires a spectroradiometer and lots of time and money.
If it's a standard incandescent bulb, a diffraction grating gets you the spectrum, but you'll need the relative spectral output at each wavelength, which is what allows you to figure out the color temperature.
What is the specific need, e.g., what is the applicability of the information?
Are you looking for color temperature? Color temperatures of typical incandescent bulbs are all considerably lower than something like the 2856 K bulb used in high performance electro-optical testing.
TTFN