We report the effect of relaxation-type self-induced temperature oscillations in the system of two parallel plates of SiO2 and VO2 which exchange heat by thermal radiation in vacuum. The non-linear feedback in the self-oscillating system is provided by metal-insulator transition in VO2. Using the method of fluctuational electrodynamics, we show that under the action of an external laser of a constant power, the temperature of VO2 plate oscillates around its phase transition value. The period and amplitude of oscillations depend on the geometry of the structure. We found that at 500 nm vacuum gap separating bulk SiO2 plate and 50 nm thick VO2 plate, the period of self-oscillations is 2 s and the amplitude is 4 K, which is determined by phase switching at threshold temperatures of phase transition.