  We report the effect of relaxation-type self-induced temperature oscillations
in the system of two parallel plates of SiO$_2$ and VO$_2$ which exchange heat
by thermal radiation in vacuum. The non-linear feedback in the self-oscillating
system is provided by metal-insulator transition in VO$_2$. Using the method of
fluctuational electrodynamics we show that under the action of an external
laser of a constant power, the temperature of VO$_2$ 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 SiO$_2$ plate and 50 nm thick VO$_2$ 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.
