A model for the numerical calculation of the effect of surface heating on the diffraction efficiency of an acousto-optic Bragg cell is presented. The temperature distribution is obtained by fitting the boundary conditions at the surface of the crystal with a solution consisting of a two dimensional Fourier series multiplied by a hyperbolic sin function in the third dimension. Calculated temperature contours for an example are shown. We also present equations for obtaining the complex amplitude of the diffracted wave and the diffraction efficiency resulting from the interaction of an optical light beam of limited cross section with the aberrated acoustic wave. A prediction of the decrease in the diffraction efficiency of a heated PbMoO4 Bragg cell is given.