Our current understanding of global mean near-surface (land and sea) air temperature (GMSAT) during the Cenozoic era relies on paleo-proxy estimates of deep-sea temperature combined with assumed relationships between global mean deep-sea temperature (GMDST), global mean sea-surface temperature (GMSST), and GMSAT. The validity of these assumptions is essential in our understanding of past climate states such as the Early Eocene Climate Optimum hothouse climate (EECO, 56–48 Ma). The EECO remains relevant today, because EECO-like CO2 levels are possible in the 22nd century under continued high CO2 emissions. We analyze the relationship between the three global temperature indicators for the EECO using 25 different millennia-long model simulations with varying CO2 levels from the Deep-Time Model Intercomparison Project (DeepMIP). The model simulations show limited spatial variability in deep-sea temperature, indicating that local temperature estimates can be regarded representative of GMDST. Linear regression analysis indicates that compared to GMSST, both GMDST and GMSAT respond more strongly to changes in atmospheric CO2 by factors of 1.18 and 1.17, respectively. Consequently, this model-based analysis validates the assumption that changes in GMDST can be used to estimate changes in GMSAT during the EECO. Paleo-proxies of GMDST, GMSST, and GMSAT during EECO show the best fit with model simulations having an atmospheric CO2 level of 1,680 ppm, which matches paleo-proxies of atmospheric CO2 during EECO. Similar analyses of other past climate states are needed to examine whether these results are robust throughout the Cenozoic, providing insight into the long-term future warming under various shared socioeconomic pathways.

Clumped isotope thermometry can independently constrain the formation temperatures of carbonates, but a lack of precisely temperature-controlled calibration samples limits its application on aragonites. To address this issue, we present clumped isotope compositions of aragonitic bivalve shells grown under highly controlled temperatures (1‒18 deg C), which we combine with clumped isotope data from aragonites precipitated in a wide range of temperatures (1‒850 deg C). We observe no offset in clumped isotope values between aragonitic foraminifera, mollusks, and abiogenic aragonites or between aragonites and calcites, eliminating the need for need for a mineral-specific calibration or acid fractionation factor. However, due to non-linear behavior of the clumped isotope thermometer, including high-temperature (>100 deg C) datapoints in linear clumped isotope calibrations causes them to underestimate temperatures of cold (1‒18 deg C) carbonates by 2.7 +/- 2.0 deg C (95% confidence level). Therefore, clumped isotope-based paleoclimate reconstructions should be calibrated using samples with well constrained formation temperatures close to those of the samples.