Despite recent advances, the link between the evolution of atmospheric CO₂ and climate during the Eocene greenhouse remains uncertain. In particular, modelling studies suggest that in order to achieve the global warmth that characterised the early Eocene, warmer climates must be more sensitive to CO₂ forcing than colder climates. Here, we test this assertion in the geological record by combining a new high-resolution boron isotope-based CO₂ record with novel estimates of Global Mean Temperature. We find that Equilibrium Climate Sensitivity (ECS) was indeed higher during the warmest intervals of the Eocene, agreeing well with recent model simulations, and declined through the Eocene as global climate cooled. These observations indicate that the canonical IPCC range of ECS (1.5 to 4.5 °C per doubling) is unlikely to be appropriate for high-CO₂ warm climates of the past, and the state dependency of ECS may play an increasingly important role in determining the state of future climate as the Earth continues to warm.