The Early Eocene, a period of elevated atmospheric CO2 (>1000 ppmv), is considered an analog for future climate. Previous modeling attempts have been unable to reproduce major features of Eocene climate indicated by proxy data without substantial modification to the model physics. Here, we present simulations using a state-of-the-art climate model forced by proxy-estimated CO2 levels that capture the extreme surface warmth and reduced latitudinal temperature gradient of the Early Eocene and the warming of the Paleocene-Eocene Thermal Maximum. Our simulations exhibit increasing equilibrium climate sensitivity with warming and suggest an Eocene sensitivity of more than 6.6°C, much greater than the present-day value (4.2°C). This higher climate sensitivity is mainly attributable to the shortwave cloud feedback, which is linked primarily to cloud microphysical processes. Our findings highlight the role of small-scale cloud processes in determining large-scale climate changes and suggest a potential increase in climate sensitivity with future warming.