In a time of multiplying international problems that require scientific input, a well-functioning science-diplomacy interface is vital for the success of global governance. The case of climate change offers valuable lessons concerning current institutional design patterns of this interface, building on more than two decades of experience with of the Intergovernmental Panel on Climate Change (IPCC) and the United Nations Framework Convention on Climate Change (UNFCCC). In this chapter I depart from the usual approach to analysing the role of science in diplomacy. Instead of assessing the functioning and processes of the IPCC, I use a cognitive perspective to analyse how diplomats’ minds receive and make use of scientific knowledge. Using interview data from 2012, I argue that: (1) most negotiation participants use a very basic and limited set of insights about climate change that has not changed significantly for a long time; (2) that recent scientific concepts — most notably the idea of climatic tipping points — are not yet part of most diplomats’ belief systems; and (3) that hardly any negotiator is able to imagine qualitatively different long-term futures that have been affected by climate change, and to link present decisions to those possible futures. I discuss the implications of these findings for the negotiation process and outline possible ways to improve the design of the science-diplomacy interface to address present cognitive limitations.