We used the ‘Radiative-Convective Model of the Earth-atmosphere system’ (OGIM) to investigate the cooling effects induced by sulphur injections into the stratosphere. The ensemble of numerical calculations was based on the A1B scenario from the IPCC Special Report on Emissions Scenarios (SRES). Several geoengineered scenarios were analysed, including the abrupt interruption of these injections in different scenarios and at different dates. We focused on the surface air temperature (SAT) anomalies induced by stratospheric sulphate aerosol generated in order to compensate future warming. Results show that continuous deployment of sulphur into the stratosphere could induce a lasting decrease in SAT. Retaining a constant aerosol loading equivalent to 6 TgS would delay the expected global warming by 53 years. Keeping the SAT constant in a context of increasing greenhouse gases (GHGs) means that the aerosol loading needs to be increased by 1.9% annually. This would offset the effect of increasing GHG under the A1B scenario. A major focus of this study was on the heating rates of SAT that would arise in different scenarios in case of an abrupt cessation of sulphur injections into the stratosphere. Our model results show that heating rates after geoengineering interruption would be 15–28 times higher than in a case without geoengineering, with likely important consequences for life on Earth. Larger initial sulphate loadings induced more intense warming rates when the geoengineering was stopped at the same time. This implies that, if sulphate loading was increased to maintain constant SAT in the light of increasing GHG concentrations, the later the geoengineering interruption was to occur, the higher the heating rates would be. Consequently, geoengineering techniques like this should only be regarded as last-resort measures and require intense further research should they ever become necessary.