The article describes the issue of gas turbine cooling after operation. Due to natural convection, an asymmetric temperature distribution occurs in the double annulus, which has a significant effect on the thermal bow of the rotor. At the same time, the desire to minimize radial clearances as this brings the advantage of higher engine efficiency is nowadays essential. On the other hand, it also requires the ability to understand and predict the cooling transient to avoid critical failures during engine restart. Based on a real engine, an experimental facility was designed to represent a simplified double annulus flow path in a section of the turbine flow path. Experimental measurements were performed and a computational model of natural convective flow during gas turbine cooling was developed. The time dependence of the temperature fields was observed and compared with computational model. Furthermore, the dependence of the temperature differences between the upper and lower double annulus was presented. The computational study is carried out with different geometrical setups, which were also validated by experimental measurements. It is shown that the thermal gradient of the rotor due to natural convection can be significantly affected by the choice of geometry and other constraints in this region. The results of the study showed several options to mitigate the rotor bow of a gas turbine. The applicability of the results may have a significant influence on the design and development of gas turbines nowadays.