Some of the most influential explorations of low-carbon transformations are conducted with Integrated Assessment Models (IAMs). The recent attempts by the IPCC to look for pathways compatible with the 1.5 °C and 2 °C temperature goals are a case in point. Earlier scholarship indicates that model-based pathways are persuasive in bringing specific possible future alternatives into view and guiding policymaking. However, the process through which these shared imaginations of possible futures come about is not yet well understood. By closely examining the science-policy dynamics around the IPCC SR1.5, we observe a sequence of mutually legitimising interactions between modelling and policy making through which the 1.5 °C goal gradually gained traction in global climate politics. Our findings reveal a practice of ‘political calibration’, a continuous relational readjustment between modelling and the policy community. This political calibration is indicative of how modellers navigate climate politics to maintain policy relevance. However, this navigation also brings key dilemmas for modellers, between 1) requirements of the policy process and experts’ conviction of realism; 2) perceived political sensitivities and widening the range of mitigation options; and 3) circulating crisp storylines and avoiding policy-prescriptiveness. Overall, these findings call into question the political neutrality of IAMs in its current position in the science-policy interface and suggest a future orientation in which modellers aim to develop additional relations with a broader set of publics resulting in more diverse perspectives on plausible and desirable futures.@en