Enhanced ocean heat transport into the Arctic is linked to stronger future Arctic warming and polar amplification. To quantify the impact of ocean heat transport on Arctic climate, it is imperative to understand how its magnitude and the associated mechanisms change in other climate states. This paper therefore assesses the ocean heat transport into the Arctic at 70∘N for climates forced with a broad range of carbon dioxide concentration levels, ranging from one-fourth to four times modern values. We focused on ocean heat transports through the Arctic entrances (Bering Strait, Canadian Archipelago, and Nordic Seas) and identified relative contributions of volume and temperature to these changes. The results show that ocean heat transport differences across the five climate states are dominated by heat transport changes in the Nordic Seas, although in the warmest climate state heat transport through the Bering Strait plays an almost equally important role. This is primarily caused by changes in horizontal currents owing to anomalous wind responses and to differential advection of thermal anomalies. Changes in sea ice cover play a prominent role by modulating the surface heat fluxes and the impact of wind stresses on ocean currents. The Atlantic meridional overturning circulation and its associated heat transport play a more modest role in the ocean heat transport into the Arctic. The net effect of these changes is that the poleward ocean heat transport at 70∘N strongly increases from the coldest climate to the warmest climate state.