Algorithms – instructions for acting on data, executed by code – are increasingly being enrolled into climate policy governance via the prediction of policy outcomes, the evaluation of climate mitigation and adaptation strategies, and the design of practitioner actions. Yet the political implications of these technological changes in environmental governance are only just beginning to be theorised. In this paper, we examine one particular facet of this emerging politics: the relationship between thinking algorithmically and hegemonic power. Drawing from Laclau and Mouffe’s theorisation of hegemony we argue that algorithmic forms of reasoning lend themselves towards producing hegemonising knowledge regimes, with important implications for a democratic politics of climate change. Recognising that algorithms stand for wider socio‐technical assemblages that structure and create knowledge, we call for greater attention to the reliance on algorithms within climate governance – less for the algorithms themselves than for their particular epistemic commitments that create algorithmic ways of thinking, with associated claims to power. Through a critical review of scholarship at the intersection of critical digital studies and environmental governance, we first identify three key epistemic commitments involved in thinking algorithmically: induction, abstraction, and optimisation. We then examine the correspondence between these key features of algorithmic thinking and the conditions that Laclau and Mouffe propose form the grounds for hegemony: objectivity, universality, and necessity. Better understanding what “thinking algorithmically” entails, and the forms of knowing and acting that it affords and excludes, is vital, we argue, to begin naming the political implications and transformative potential of new forms of climate governance.