The reverse Pluronic, triblock copolymer 17R4 is formed from poly(propylene oxide) (PPO) and poly(ethylene oxide) (PEO): PPO14 - PEO24 - PPO14, where the number of monomers in each block is denoted by the subscripts. In water, 17R4 has a micellization line marking the transition from a unimer network to self-aggregated spherical micelles which is quite near a cloud point curve above which the system separates into copolymer-rich and copolymer-poor liquid phases. The phase separation has an Ising-like, lower consolute critical point with a well-determined critical temperature and composition. We have measured the heat capacity as a function of temperature using an adiabatic calorimeter for three compositions: (1) the critical composition where the anomaly at the critical point is analyzed, (2) a composition much less than the critical composition with a much smaller spike when the cloud point curve is crossed, and (3) a composition near where the micellization line intersects the cloud point curve that only shows micellization. For the critical composition, the heat capacity anomaly very near the critical point is observed for the first time in a Pluronic/water system and is described well as a second-order phase transition resulting from the copolymer-water interaction. For all compositions, the onset of micellization is clear, but the formation of micelles occurs over a broad range of temperatures and never becomes complete because micelles form differently in each phase above the cloud point curve. The integrated heat capacity gives an enthalpy that is smaller than the standard state enthalpy of micellization given by a van't Hoff plot, a typical result for Pluronic systems.