The heating of a cylindrical sample in a monoellipsoidal mirror furnace is considered. A radiation model is formulated for slender samples where the radiative exchange between the sample and the mirror is studied analytically. To analyse the behavior of the model, the temperature field in the sample is calculated using a one-dimensional conduction-radiation model. The differences with respect to a model where the radiative exchange is not considered are not only quantitative but qualitative. The model predicts a strongly asymmetric heating, which may cause asymmetries in the grown crystal as observed experimentally. Comparison with experimental data is made.