The Paris Agreement, related intergovernmental decisions, and transnational climate change governance initiatives mobilize data as a means of measuring, managing, and addressing changing climatic conditions. At the same time, the Paris Agreement formally acknowledges the human rights implications of the unfolding climate crisis. Given the reliance on data and rights in climate change governance, the aim of this article is twofold. Firstly, it analyzes how processes of datafication at transnational and local levels promise, yet struggle, to render the climate governable. Secondly, the article critically reflects on the capacity of human rights to complement datafied governance processes meaningfully – specifically, in what ways rights can (and cannot) alleviate local concerns regarding datafication. Methodologically, the article develops a perspective that foregrounds situated sense-making and experience in place. It is based on an empirical case study of the Global Covenant of Mayors for Climate & Energy, a transnational alliance of cities that have committed to working towards the goals of the Paris Agreement; and it engages with ethnographic literature that conceptualizes rights as lived forms of meaning-making, articulation, struggle, and resistance. Attending to place, the article confronts problematic assumptions about the universality, neutrality, and representativeness of data and rights, raising critical questions about their capacity to ‘govern’ climate change.