Sea ice is a critical component of the polar and global climate that demands reliable future projections. Yet, such projections continue to suffer from uncertainties largely associated with inter-model spread. Global ocean heat transport (OHT) has been hypothesised as a source of this uncertainty, as simulations with greater OHT into the polar regions tend to exhibit greater historical and future sea ice loss. Previous studies have identified such intuitive correlations but stop short of a physical explanation needed to attribute model spread in sea ice to the ocean. Here, we explain the sign and size of the emergent sensitivity of sea ice to OHT using a simple equation that we derive from an idealised energy-balance model. This equation reveals underlying mechanisms involving the atmosphere and captures the OHT–sea ice relationship in climate models. Future Arctic sea ice loss is regulated by changes in OHT, the impact of which is set by compensation of atmospheric heat transport and radiative feedbacks. Our results suggest that addressing ocean biases in climate models will substantially reduce uncertainty in projections of sea ice and the global climate state.