Do you know a reference in the literature that gives straightforward conversion formulae between stellar color indices and effective temperatures for the broad range of spectral types and luminosities?
Look at the un-numbered equation after equation (33) in Astronomy and Astrophysics 426, 297-307 (2004). You will need the coefficients in the on-line materials at http://www.edpsciences.org
Yes there are lots of papers that contain relationships between colours and effective temperatures. Some of them even try to take into account any dependence on metallicityor surface gravity. I think the calibrations are quite good for solar type stars and warmer. There are still problems and uncertainties with the temperature-colour relationships for cooler M-dwarfs.
You could look at Pecaut & Mamajek 2013, ApJS, 208, 9 which gives these relationships for main sequence and pre main sequence stars.
Or there are the older papers by Kenyon & Hartmann, 1995, ApJS, 101, 117 or perhaps Alonso et al. 1999, A&AS, 140, 261
The best way to derive these relationships is by using the colours of stars with known radii, distances, luminosities and hence effective temperatures. There are relatively few such stars, but you could look at Boyajian et al. 2012, ApJ, 746, 101 and 2012, ApJ, 757, 112
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