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Facing climate change, public action relies on research based on hypotheses concerning future effects that will have to be dealt with. Using a conception of climate change seen as an ongoing development encompassing—in space and in time—public action, we explore, by looking at thirty years of warning practices, the relations between the evolution of extreme heat waves and the transformation of the public management of heat waves in public policy on climate change adaptation. It appears that a change of phase is taking place, in the sense of a change in the lasting constraints taken into account by public policy makers to manage heat waves. This shift is marked by the gradual emergence of an anticipation constraint, supplementing previously predominant reaction constraints. The integration of this additional constraint was itself anticipated by the atypical law of January 2001 dealing with greenhouse gases. Based on this development, we discuss the role of climate knowledge in the evolution of the methods of implementing public policies on climate change adaptation and propose suggestions for public management in the extreme context resulting from climate change.