Decision-making for climate change adaptation requires an integrated and cross-sectoral approach to adequately capture the complexity of interconnected systems. More meaningful decisions can be taken in an arena where different agents provide knowledge of specific domains. This paper uses a semi-quantitative method based on cognitive mapping to demonstrate how new knowledge emerges when combining knowledge from diverse agents. For the case of heatwaves in the city of Madrid (Spain) we elicit knowledge about climatic impacts across urban sectors and potential adaptation options. Knowledge is elicited in individual interviews and then aggregated using fuzzy cognitive maps. We observe that the individual maps vary considerably in size and structure and find evidence of diverse and even contradictory perceptions. There is no “super-stakeholder”, who theoretically could provide full knowledge about mechanisms operating in this urban system: the maximum percentage of the final aggregated map explained by a single individual is 26% in terms of concepts and 13% in terms of connections. We illustrate how the emergence of new knowledge can be sustained by combining scientific and policy expertise. Our approach supports knowledge co-production and allows to account for the interconnectedness of urban sectors under climatic impacts in view of formulating more robust adaptation strategies.