Global mean surface temperatures are rising in response to anthropogenic greenhouse gas emissions. The magnitude of this warming at equilibrium for a given radiative forcing - referred to as specific equilibrium climate sensitivity (S) - is still subject to uncertainties. Here we estimate global mean temperature variations and S using a 784,000-year-long field reconstruction of Sea Surface Temperatures (SST) and a transient paleo-climate model simulation. Our results reveal that S is strongly dependent on the climate background state with significantly larger values attained during warm phases. Using the Representative Concentration Pathway 8.5 for future greenhouse radiative forcing, we find that the range of paleo-based estimates of earth's future warming by year 2100 CE overlaps with the upper range of climate simulations conducted as part of the Coupled Model Intercomparison Project, phase 5 (CMIP5). Furthermore, we find that within the 21st century global mean temperatures will very likely exceed maximum levels reconstructed for the last 784,000 years. Based on temperature data from eight glacial cycles, our results provide an independent validation of the magnitude of current CMIP5 warming projections.