The Bjerknes compensation (BJC) under global warming is studied using a simple box model and a coupled Earth system model. The BJC states the out-of-phase changes in the meridional atmosphere and ocean heat transports. Results suggest that the BJC can occur during the transient period of global warming. During the transient period, the sea ice melting in the high latitudes can cause a significant weakening of the Atlantic meridional overturning circulation (AMOC), resulting in a cooling in the North Atlantic.