Astrometric surveys provide the opportunity to measure the absolute magnitudes of large numbers of stars, but only if the individual line-of-sight extinctions are known. Unfortunately, extinction is highly degenerate with stellar effective temperature when estimated from broad band optical/infrared photometry. To address this problem, I introduce a Bayesian method for estimating the intrinsic parameters of a star and its line-of-sight extinction. It uses both photometry and parallaxes in a self-consistent manner in order to provide a non-parametric posterior probability distribution over the parameters. The method makes explicit use of domain knowledge by employing the Hertzsprung--Russell Diagram (HRD) to constrain solutions and to ensure that they respect stellar physics. I first demonstrate this method by using it to estimate effective temperature and extinction from BVJHK data for a set of artificially reddened Hipparcos stars, for which accurate effective temperatures have been estimated from high resolution spectroscopy. Using just the four colours, we see the expected strong degeneracy (positive correlation) between the temperature and extinction. Introducing the parallax, apparent magnitude and the HRD reduces this degeneracy and improves both the precision (reduces the error bars) and the accuracy of the parameter estimates, the latter by about 35%. The resulting accuracy is about 200K in temperature and 0.2mag in extinction. I then apply the method to estimate these parameters and absolute magnitudes for some 47000 F,G,K Hipparcos stars which have been cross-matched with 2MASS. The method can easily be extended to incorporate the estimation of other parameters, in particular metallicity and surface gravity, making it particularly suitable for the analysis of the 10^9 stars from Gaia.