As a large civil gas turbine is cooling following operation, natural convective flows cause components to cool asymmetrically—the bottom sector cools faster than the top sector. This can lead to a number of issues that have the potential to damage engine components and affect operability. The ability to predict and understand this transient cooling cycle of a gas turbine has proven to be extremely difficult, owing to the complex nature of natural convective flow physics and its dependency on a considerable number of design parameters. An experimental and numerical investigation into the impact of axial ventilation (interaction between the annulus and the external air) and blade rows on the natural convective flow field in a large civil gas turbine high-pressure compressor has led to some key discoveries. Axial ventilation caused a 70% increase in the peak top-to-bottom temperature difference in the cooling cycle, when compared to the baseline sealed case. The combinations of four blade rows and axial ventilation caused a 130% increase in peak temperature difference over the baseline case. Numerical simulations illuminated that the root cause of this was the cold air drawn into the lower section of the annulus led to a relatively high heat flux, coupled with a blockage effect on the natural draft in the upper section of the annulus inhibiting the convective heat transfer from this section. There appears to be a relationship between the porosity of the annulus and the peak top-to-bottom temperature difference that was observed. This study on the impact of two parameters on the shutdown cooling of a simplified gas turbine annulus has highlighted their importance and inter-dependency in defining the level of rotor bow that is observed. Therefore, it is imperative that these effects are included and sufficiently captured in order for a shutdown cooling prediction method to be accurate.