Abstract We construct an upper ocean (0–1000 m) North Atlantic heat budget (26°–67°N) for the period 1950–2020 using multiple observational datasets and an eddy-permitting global ocean model. On multidecadal time scales, ocean heat transport convergence controls ocean heat content (OHC) tendency in most regions of the North Atlantic with little role for diffusive processes. In the subpolar North Atlantic (45°–67°N), heat transport convergence is explained by geostrophic currents, whereas ageostrophic currents make a significant contribution in the subtropics (26°–45°N). The geostrophic contribution in all regions is dominated by anomalous advection across the time-mean temperature gradient although other processes make a significant contribution, particularly in the subtropics. The time scale and spatial distribution of the anomalous geostrophic currents are consistent with a simple model of basin-scale thermal Rossby waves propagating westward/northwestward in the subpolar gyre, and multidecadal variations in regional OHC are explained by geostrophic currents periodically coming into alignment with the mean temperature gradient as the Rossby wave passes through. The global ocean model simulation shows that multidecadal variations in the Atlantic meridional overturning circulation are synchronized with the ocean heat transport convergence consistent with modulation of the west–east pressure gradient by the propagating Rossby wave. Significance Statement The purpose of the work is to understand why the North Atlantic Ocean warms up and cools down on time scales of about 40 years. The key finding is that the temperature fluctuations are caused by an oceanic wave pushing the ocean surface up and down and causing ocean currents to change direction, pushing heat into and out of different parts of the ocean, and drawing down or emitting heat to the atmosphere. The findings matter because the warm and cool periods affect the climate of the countries surrounding the North Atlantic. Climate models need to account for this oceanic wave process to correctly predict how it will change in the future and affect the large-scale climate in a warming world.