There is broad evidence of climate change causing shifts in fish distribution worldwide, but less is known about the response of fisheries to these changes. Responses to climate‐driven shifts in a fishery may be constrained by existing management or institutional arrangements and technological settings. In order to understand how fisheries are responding to ocean warming, we investigate purse seine fleets targeting tropical tunas in the east Atlantic Ocean using effort and sea surface temperature anomaly (SSTA) data from 1991 to 2017. An analysis of the spatial change in effort using a centre of gravity approach and empirical orthogonal functions is used to assess the spatiotemporal changes in effort anomalies and investigate links to SSTA. Both analyses indicate that effort shifts southward from the equator, while no clear pattern is seen northward from the equator. Random forest models show that while technology and institutional settings better explain total effort, SSTA is playing a role when explaining the spatiotemporal changes of effort, together with management and international agreements. These results show the potential of management to minimize the impacts of climate change on fisheries activity. Our results provide guidance for improved understanding about how climate, management and governance interact in tropical tuna fisheries, with methods that are replicable and transferable. Future actions should take into account all these elements in order to plan successful adaptation.