An analytical solution for the temperature distribution in freely radiating crystals has been developed. It was possible to solve this problem, within the growing crystal, because the heat transfer due to radiation was small as compared with the heat transfer due to conduction. The solution was applied to the growth of silicon crystals grown by the floating-zone method and the results were found to be in good agreement with experimental data. It is shown that the influence of the crystal growth rate on the temperature profile must be included, when it is higher than 1–2 mm/min. The longitudinal temperature gradient at a concave solid- liquid interface was found to vary in a characteristic manner with the distance from the axis. A similar variation was observed for the height of the defect area formed at the solid-liquid interface in quenched silicon crystals.