Future global warming from anthropogenic greenhouse gas emissions will depend on climate feedbacks, the effect of which is expressed by climate sensitivity, the warming for a doubling of atmospheric CO2 content. It is not clear how feedbacks, sensitivity, and temperature will evolve in our warming world, but past warming events may provide insight. Here we employ paleoreconstructions and new climate-carbon model simulations in a novel framework to explore a wide scenario range for the Paleocene-Eocene Thermal Maximum (PETM) carbon release and global warming event 55.8Ma ago, a possible future warming analogue. We obtain constrained estimates of CO2 and climate sensitivity before and during the PETM and of the PETM carbon input amount and nature. Sensitivity increased from 3.3-5.6 to 3.7-6.5K (Kelvin) into the PETM. When taken together with Last Glacial Maximum and modern estimates, this result indicates climate sensitivity increase with global warming.