If climate change affects pollinator-dependent crop production, this will have important implications for global food security because insect pollinators contribute to production for 75% of the leading global food crops. We investigate whether climate warming could result in indirect impacts upon crop pollination services via an overlooked mechanism, namely temperature-induced shifts in the diurnal activity patterns of pollinators. Using a large data set on bee pollination of watermelon crops, we predict how pollination services might change under various climate change scenarios. Our results show that under the most extreme IPCC scenario (A1F1), pollination services by managed honey bees are expected to decline by 14.5%, whereas pollination services provided by most native, wild taxa are predicted to increase, resulting in an estimated aggregate change in pollination services of +4.5% by 2099. We demonstrate the importance of native biodiversity in buffering the impacts of climate change, because crop pollination services would decline more steeply without the native, wild pollinators. More generally, our study provides an important example of how biodiversity can stabilize ecosystem services against environmental change.