Scientific climate knowledge is often argued to be a key ingredient in climate adaptation. Focusing on individual sectors and institutions, researchers have given insights as to how climate knowledge is reframed according to institutional cultures and priorities. This study extends such scholarship by comparing how four sectors—greenspace management, building technology, spatial planning, and health—perceive, judge, transfer, and appropriate knowledge on urban heatwaves, and what adaptation options are proposed. Based on semi-structured interviews, documentary materials and observations of two workshops collected in two Swiss cities, I draw on Eviatar Zerubavel and his ‘cultural cognitive sociology’ whose work emphasises how collectively shared patterns of recognition and thinking guide and facilitate human judgement. I find two factors to influence knowledge appropriation. On the one hand, the formative dimension of knowledge underscores that experts understand climate knowledge similarly when a sector shares key concepts with climate science. If such ‘cognitive links’ are missing, the answers on how heatwaves impact experts’ work are more varied. On the other hand, the performative dimension of knowledge highlights that experts’ eagerness to adapt is influenced by diverging technical, legal, and social possibilities. When experts’ decision scope is large, then uptake of climate knowledge is more fluid. With a more explicit understanding of why sectors differ in their appropriation and integration of climate knowledge into their work, this study is a reminder that only fitting knowledge is of value to sectoral experts.