When a gas undergoes an exothermic reaction in a closed vessel, spatial temperature gradients can develop. If these gradients become sufficiently large, the resulting buoyancy forces will move the gas, i.e. there is natural convection. The nature of the resulting flow is determined by the Rayleigh number, Ra = (β g ΔT L^3) / (κ ν). The evolution of such a system will depend on the interactions of natural convection, diffusion of both heat and chemical species, and chemical reaction. This study is concerned with a gas-phase system undergoing Sal’nikov’s reaction: P → A → B, in the presence of natural convection. This kinetic scheme is used as a simplified representation of a cool flame, which is a feature of the low temperature combustion of a hydrocarbon vapour. Sal’nikov’s reaction is one of the simplest to display thermokinetic oscillations, such as those seen in cool flames. The behaviour of Sal’nikov’s reaction in the presence of natural convection was investigated using a combination of analytical and numerical techniques. First, a numerical model was developed to compute the temperature, velocity and concentrations when a simple exothermic reaction occurs in a spherical batch reactor, the results of which could be compared with previous experimental measurements. Subsequently, a scaling analysis of Sal’nikov’s reaction proceeding in a spherical reactor was performed. This yielded significant insight into the general behaviour of this and similar systems. The forms of the analytical scales were confirmed through comparison with the results from numerical simulations. These scales were used to predict how the system responds to changes in certain key process variables, such as the pressure and the size of the reactor. It was shown that the behaviour of this system is governed by the ratios of the characteristic timescales for diffusion, reaction and natural convection. These ratios were used to define a regime diagram describing the system. The behaviour in different parts of this regime diagram was characterised and regions in which oscillations occur were identified.