Estimates of global mean near‐surface air temperature (global SAT) for the Cenozoic era rely largely on paleo‐proxy data of deep‐sea temperature (DST), with the assumption that changes in global SAT covary with changes in the global mean deep‐sea temperature (global DST) and global mean sea‐surface temperature (global SST). We tested the validity of this assumption by analyzing the relationship between global SST, SAT, and DST using 25 different model simulations from the Deep‐Time Model Intercomparison Project simulating the early Eocene Climatic Optimum (EECO) with varying CO2 levels. Similar to the modern situation, we find limited spatial variability in DST, indicating that local DST estimates can be regarded as a first order representative of global DST. In line with previously assumed relationships, linear regression analysis indicates that both global DST and SAT respond stronger to changes in atmospheric CO2 than global SST by a similar factor. Consequently, this model‐based analysis validates the assumption that changes in global DST can be used to estimate changes in global SAT during the early Cenozoic. Paleo‐proxy estimates of global DST, SST, and SAT during EECO show the best fit with model simulations with a 1,680 ppm atmospheric CO2 level. This matches paleo‐proxies of EECO atmospheric CO2, indicating a good fit between models and proxy‐data. Plain Language Summary The global mean surface temperature is a commonly used indicator to measure global climate change. Our understanding of how the global surface temperature has changed in the last 66 Myr is mainly based on the assumption that changes in the deep‐sea temperature (DST) reflect changes at the surface well. Here, we test this idea by using climate model simulations of a hothouse period, the early Eocene Climate Optimum (53–49 Myr ago). We find that changes in the global DST indeed correlate well with temperature changes at the surface. We find the best fit between the models and data from the early Eocene for atmospheric CO2 levels at around 1,680 ppm. Key Points In early Eocene model simulations (Deep‐Time Model Intercomparison Project DeepMIP), global mean deep‐sea, and surface temperatures are equally sensitive to atmospheric CO2 changes Model‐simulated deep‐sea temperatures show limited spatial variability, making local estimates generally representative of the global mean The model simulations with a CO2 forcing of 1,680 ppm match paleo‐proxies of global mean deep‐sea, sea‐surface, and surface temperature