This dataset contains derived annual mean globally averaged variables from an existing global coupled carbon-climate Earth System Model and a novel atmosphere-ocean box model to understand surface warming response in terms of changes in global carbon inventories, empirical heat budget, and variation in time with carbon emissions. The source model outputs were generated by Thomas Froelicher in 2015 using a 1000-year simulation of the global coupled carbon-climate Earth System Model developed at the Geophysical Fluid Dynamics Laboratory (GFDL ESM2M). A scenario was forced of a 1% annual rate increase in carbon dioxide from preindustrial levels until global mean surface air temperature increased by 2 degrees Celsius since the preindustrial, after this point emissions of carbon were set to zero and all other non-carbon dioxide greenhouse gases were kept at preindustrial levels. Output parameters included: ocean temperature; salinity; dissolved inorganic carbon; ocean alkalinity; dissolved inorganic phosphate; surface air temperature; atmospheric carbon dioxide and cumulative carbon emission. Annual mean variables were then derived from these data. This was determined by calculated changes in: ocean carbon inventory; ocean carbon under saturation; saturated dissolved inorganic carbon; ocean dissolved inorganic carbon; radiative forcing from carbon dioxide; and ocean heat uptake. Additionally the dependence of radiative forcing on carbon emissions, dependence of surface warming on radiative forcing and surface warming dependence on radiative forcing were determined. The box model consists of three homogeneous layers: a well‐mixed atmosphere; an ocean mixed layer with 100‐m thickness; and an ocean interior with 3,900‐m thickness, all assumed to have the same horizontal area. The model solves for the heat and carbon exchange between these layers, including physical and chemical transfers, however ignoring biological transfers, and sediment and weathering interactions. The model is forced from an equilibrium by carbon emitted into the atmosphere with a constant rate of 20 PgC/year for 100 years and integrated for 1,000 years. Ocean ventilation is represented by the ocean interior taking up the heat and carbon properties of the mixed layer on an e-folding time scale of 200 years. These datasets were generated as part of the Natural Environment Research Council (NERC) Discovery Science project “Mechanistic controls of surface warming by ocean heat and carbon uptake” standard grant reference NE/N009789/1 lead by Principal Investigator - Professor Ric Williams, University of Liverpool and Co-Investigator - Dr Philip Goodwin, University of Southampton. Data are acrvhived at the British Oceanographic Data Centre.