The increase in sea surface temperature (SST) is one of the primary consequences of climate change and has the potential to impact tuna fisheries. This paper theoretically models and then applies the production function approach to establish a positive but non-linear relationship between catch and SST using gridded data for yellowfin and skipjack tuna catch in the Eastern Pacific Ocean. We test different forms of relationship between SST and the carrying capacity of tuna fisheries. By considering area, species and fishing methods, we provide spatially and biologically relevant information for the management of tuna in response to warming oceans. The increase in yellowfin tuna catch is higher in the Northern Hemisphere compared to the Southern Hemisphere, while the reverse is true for skipjack tuna. We also find that there is a nonlinear (i.e. logarithmic and quadratic) relationship between the SST and the carrying capacity of tuna fisheries.