When discussing stars, theorists tend to use effective temperature $T_\text{eff}$ and luminosity $L$ (on logarithmic scales). Observers, on the other hand, usually talk about observed colours and magnitudes (e.g. $B$ vs. $B{-}V$). These two sets of parameters are obviously related. Temperature corresponds to colour; luminosity to magnitude.

How does one transform between them? That is, given $L$ and $T_\text{eff}$ (from which one can derive $R$ through $L=4\pi R^2\sigma T_\text{eff}^4$), what are $B$ and $B{-}V$, or any other colour/magnitude? Alternatively, given $B$ and $B{-}V$, what are $L$ and $T_\text{eff}$? I figure $(L,T_\text{eff})\to(B,B{-}V)$ is easier.

I'll start trying to answer it myself just by presuming the star is emitting a blackbody spectrum and integrating against the $B$ and $V$ filter functions. I realise this will be a major simplification but it's a start. I'm hoping it's been done (and published) before, maybe with better treatment of reddening etc.