Based on the thermal hysteresis of a phase change material exchanging radiative heat with a phase invariable one, we propose a radiative thermal memristor characterized by a Lissajous curve between their exchanged heat flux and temperature difference periodically modulated in time. For a memristor with terminals of VO_{2} and a blackbody, it is shown that (i) the temperature variations of its memristance follow a closed loop determined by the thermal hysteresis width of VO_{2}, and (ii) the thermal memristance on-off ratio is determined by the contrast of VO_{2} emissivities for its insulating and metallic phases and is equal to 3.6. The analogy of the proposed memristor to its electrical counterpart makes it promising to lay the foundations of the thermal computing with photons.