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Transforming global energy systems is critical for climate change mitigation and requires overcoming not only techno-economic, but also socio-technical hurdles. The main tools to analyse challenges in these two domains are integrated assessment models (IAMs) and transition theories or models, respectively. Despite a surging interest in integrative research that leverages complementarities in order to include social constraints into IAMs, both approaches are often confined to their own disciplinary background and practical integration studies of existing models are scarce. Here I demonstrate the feasibility of model integration by a bi-directional soft-link that merges the strengths of a neoclassical intertemporally optimising IAM with one global region, and a technologically and regionally highly resolved, evolutionary simulation model of S-shaped technology diffusion in the power sector. The new model iteratively converges to a stable equilibrium via two time-dependent coupling variables: carbon prices and renewable energy shares. The results for a 2 °C scenario show that due to gradual technology diffusion, energy transition challenges are exacerbated and incur higher economic losses. I discuss the potential of coupling existing models as an option to combine insights from different disciplinary perspectives to energy transitions.