The Conference of Parties to the United Nations Framework Convention on Climate Change, or COP, held annually in a different city, opens up a two-week window of opportunity for concerned actors around the globe to engage in debate on climate action where by issues are climatized. Diverse spaces are invested, including online. This was clearly the case at the occasion of COP21 in Paris, when climate change-related online communication reached extraordinary levels. Among the different sites, Twitter stands out as a particularly interesting one for studying the way people and organizations, both public and private, engage in debate on international climate politics and eventually seek to exert influence over public perceptions. In this paper we focus on the COP21 Twitter conversation as providing a particular digital “proxy” to the study of the climatization of issues. After situating this endeavour as the continuation of prior research aimed at mapping issue climatization within the COP process over 20 years on the basis of a digitalized textual corpus, we explore the specific methodological challenges pertaining to the reliance on digitally native datasets, extracted from social media platforms, to study debates on climate politics. Then, after exploring on the use of hashtaging as a means to map topical framings at the global level, we focus on the use of a dataset extracted from the French twittersphere to describe, in a qualitative approach, the ways NGOs, businesses, policy makers and the news media engaged in the COP21 conversation and seek to assess their respective strategies to exert influence on the framing of the Paris “momentum”.