This article explores the ways in which data centre operators are currently reconfiguring the systems of energy and heat supply in European capitals, replacing conventional forms of heating with data-driven heat production, and becoming important energy suppliers. Taking as an empirical object the heat generated from server halls, the article traces the expanding phenomenon of ‘waste heat recycling’ and charts the ways in which data centre operators in Stockholm and Paris direct waste heat through metropolitan district heating systems and urban homes, and valorise it. Drawing on new materialisms, infrastructure studies and classical theory of production and destruction of value in capitalism, the article outlines two modes in which this process happens, namely infrastructural convergence and decentralisation of the data centre. These modes arguably help data centre operators convert big data from a source of value online into a raw material that needs to flow in the network irrespective of meaning. In this conversion process, the article argues, a new commodity is in a process of formation, that of computation traffic. Altogether data-driven heat production is suggested to raise the importance of certain data processing nodes in Northern Europe, simultaneously intervening in the global politics of access, while neutralising external criticism towards big data by making urban life literally dependent on power from data streams.