Biomass burning aerosol (BBA) emissions in the Coupled Model Intercomparison Project Phase 6 (CMIP6) historical forcing fields have enhanced temporal variability during the years 1997–2014 compared to earlier periods. Recent studies document that the corresponding inhomogeneous shortwave forcing over this period can cause changes in clouds, permafrost, and soil moisture, which contribute to a net terrestrial Northern Hemisphere warming relative to earlier periods. Here, we investigate the ocean response to the hemispherically asymmetric warming, using a 100-member ensemble of the Community Earth System Model version 2 Large Ensemble forced by two different BBA emissions (CMIP6 default and temporally smoothed over 1990–2020). Differences between the two subensemble means show that ocean temperature anomalies occur during periods of high BBA variability and subsequently persist over multiple decades. In the North Atlantic, surface warming is efficiently compensated for by decreased northward oceanic heat transport due to a slowdown of the Atlantic Meridional Overturning Circulation. In the North Pacific, surface warming is compensated for by an anomalous cross-equatorial cell (CEC) that reduces northward oceanic heat transport. The heat that converges in the South Pacific through the anomalous CEC is shunted into the subsurface and contributes to formation of long-lasting ocean temperature anomalies. The anomalous CEC is maintained through latitude-dependent contributions from narrow western boundary currents and basin-wide near-surface Ekman transport. These results indicate that interannual variability in forcing fields may significantly change the background climate state over long timescales, presenting a potential uncertainty in CMIP6-class climate projections forced without interannual variability.