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The meridional transport of heat is a critical component of the Earth's climate system. If the total heat transported by the climate system is approximately constant, then the anomalies of heat transported by the atmosphere and ocean should be approximately equal and opposite, a scenario now called Bjerknes compensation. This has previously been found in two coupled climate models, with both showing multi-decadal variability in the heat transports. This work identifies Bjerknes compensation in the Bergen Climate Model, adding to the understanding of the robust features of Bjerknes compensation in coupled climate models. The atmospheric and oceanic heat transports are investigated in the 600-year control run of a fully-coupled global climate model. The presence of Bjerknes compensation is confirmed by the strong anti-correlation and equal magnitude of the anomalies of these heat transports. The heat transport anomalies contain a signal of multi-decadal variability. Since natural variability in global heat transport could mask anthropogenic climate change signals, understanding Bjerknes compensation is of socio-economic importance. Using regression analysis the atmospheric and oceanic responses to the multi-decadal variability of the Bjerknes compensation signal are investigated. This highlights the importance of the marginal ice zones of the Greenland and Barents Seas as the critical location for coupling the atmosphere and ocean. During periods of increased heat transport in the ocean, these regions show decreased sea-ice, leading to increased fluxes and local temperatures, and giving rise to a thermal low-pressure center and a non-local high-pressure centre, thus changing the atmospheric flow on multi-decadal timescales.