The Earth's climate is currently changing rapidly, primarily due to emissions of greenhouse gases caused by human industrialisation. These emissions are projected to increase through this century, and under some scenarios atmospheric carbon dioxide (CO2) concentrations could reach more than 1000 parts per million (ppm) by the year 2100, compared with 280 ppm prior to industrialisation. In order to predict the sociological, environmental, and economic impacts of such scenarios, and thus to better prepare for them, the only tool at our disposal is climate modelling. In order to assess our confidence in predictions from climate models, they are routinely tested under conditions of known climate. However, this testing (and associated tuning of the models) is almost exclusively carried out under modern climate conditions, and relative to recently observed climate change, for which CO2 concentrations are less than 400 ppmv. As such, our state-of-the-art climate models have never been tested under the high CO2, super-warm climate conditions to which they are primarily applied, and upon which major policy decisions are made. However, there exist time periods in Earth's deeper past (for example the Eocene, about 50 million years ago) when CO2 concentrations were similar to those expected by the end of this century; but climatological information from these time periods is currently sparse and is associated with large uncertainties, and the exact concentrations of CO2 are only poorly known. Recent changes in our understanding of how the geological record preserves climate signals, and developments in laboratory techniques, mean that for the first time there exists a new and exciting opportunity to remedy this situation and provide a much-needed evaluation of our very latest climate models in a super-warm world. In SWEET, we will apply these emerging techniques, and develop new methodologies and tools, to produce a global dataset of Eocene temperatures. Coupled with new and high-fidelity reconstructions of Eocene CO2 concentrations, and state-of-the-art maps of the 'palaeogeograpy' (continental positions, mountain ranges, ocean depths etc.), we will use this dataset to test a state-of-the art climate model under high atmospheric CO2, Eocene conditions. The model, UKESM, is identical to that being used by the UK Met Office in the international 'CMIP6' project, which itself will be the primary input to the next Intergovernmental Panel on Climate Change (IPCC) assessment report. We will also use our data and additional model simulations (running at high spatial resolution) to investigate the relative importance of the various mechanisms which determine the response of the Earth system to high CO2 and to changes in palaeogeography. A characteristic of SWEET is that we will take full account of uncertainties in the geological data and the modelling, and our model-data comparisons will be underpinned by a statistical framework which incorporates these uncertainties. We will also adopt a 'multi-proxy' approach by using several independent geological archives to reconstruct temperature. For one of these archives, namely the oxygen isotopic composition of the fossilised shells of microscopic marine creatures from the Eocene, we will apply a particularly innovative approach which will enable us to 'resurrect' previously discredited data, by using an extremely fine-scale 'ion probe' to investigate how these isotopic signatures of past climate change are recorded in individual fossils. SWEET has strong links to UK Met Office, and to the international DeepMIP project, which is part of the 'Palaeoclimate Modelling Intercomparison Project', itself part of CMIP6. We expect our results to feed into the next IPCC assessment reports and therefore to ultimately inform policy.