A theoretical approach for the auto-oscillation of radiation-induced defect density and temperature in impure crystals is developed. It is shown that at certain critical parameters of crystal properties and irradiation conditions, the steady distribution of temperature and the defect density of irradiated crystal become unstable and auto-oscillation must be observed. These oscillations are treated as the result of crystal heating due to the energy release in the processes of radiation-defect recombination and their absorption by sinks. Critical parameters and auto-oscillation frequencies have been determined. The calculations for some materials are presented.