Oxygen isotopes in marine sediments (δ 18 O) are used to reconstruct Earth’s past temperature and reveal a generally cooling climate over the Cenozoic (66Ma-present). This trend is punctuated by large multimillenial thermal extreme events, most notably the Paleocene-Eocene Thermal Maximum (56Ma). We show that the distribution of these thermal extremes is excellently captured by the generalized extreme value distribution. This then motivates its use to investigate the state-dependence of these extremes. The distribution’s shape, captured by the shape parameter ξ, changes consistently with baseline δ 18 O values, such that large thermal extremes (>3 standard deviations) are far more likely in warmer climate states. We project that anthropogenic warming has the potential to return the baseline climate state to one where large thermal extremes are substantially more likely. Short title: Thermal extreme state-dependence 66-0Ma One-Sentence Summary: Warmer baseline climate states are associated with more extreme multimillenial warming events over the past 66 million years.