Materials with strong electronic Coulomb interactions play an increasing role in modern materials applications. ''Thermochromic'' systems, which exhibit thermally induced changes in their optical response provide a particularly interesting case. The optical switching associated with the metal-insulator transition of vanadium dioxide, for example, has been proposed for use in numerous applications, ranging from anti-laser shields to ''intelligent'' windows, which selectively filter radiative heat in hot weather conditions. In this work, we develop the theoretical tools for describing such a behaviour. Using a novel scheme for the calculation of the optical conductivity of correlated materials, we obtain quantitative agreement with experiments for both phases of VO2.