Accurate estimates of past global mean surface temperature (GMST) help to contextualise future climate change and are required to estimate the sensitivity of the climate system to CO2 forcing through Earth's history. Previous GMST estimates for the latest Paleocene and early Eocene (similar to 57 to 48 million years ago) span a wide range (similar to 9 to 23 degrees C higher than pre-industrial) and prevent an accurate assessment of climate sensitivity during this extreme greenhouse climate interval. Using the most recent data compilations, we employ a multi-method experimen- tal framework to calculate GMST during the three DeepMIP target intervals: (1) the latest Paleocene (similar to 57 Ma), (2) the Paleocene-Eocene Thermal Maximum (PETM; 56 Ma), and (3) the early Eocene Climatic Optimum (EECO; 53.3 to 49.1 Ma). Using six different methodologies, we find that the average GMST estimate (66% confidence) during the latest Paleocene, PETM, and EECO was 26.3 degrees C (22.3 to 28.3 degrees C), 31.6 degrees C (27.2 to 34.5 degrees C), and 27.0 degrees C (23.2 to 29.7 degrees C), respectively. GMST estimates from the EECO are similar to 10 to 16 degrees C warmer than pre-industrial, higher than the estimate given by the Intergovernmental Panel on Climate Change (IPCC) 5th Assessment Report (9 to 14 degrees C higher than pre-industrial). Leveraging the large signal associated with these extreme warm climates, we combine estimates of GMST and CO2 from the latest Paleocene, PETM, and EECO to calculate gross estimates of the average climate sensitivity between the early Paleogene and today. We demonstrate that bulk equilibrium climate sensitivity (ECS; 66% confidence) during the latest Paleocene, PETM, and EECO is 4.5 degrees C (2.4 to 6.8 degrees C), 3.6 degrees C (2.3 to 4.7 degrees C), and 3.1 degrees C (1.8 to 4.4 degrees C) per doubling of CO2. These values are generally similar to those assessed by the IPCC (1.5 to 4.5 ffiC per doubling CO2) but appear incompatible with low ECS values (< 1 :5 per doubling CO2).