The causes of decadal variations in global warming are poorly understood, however it is widely understood that variations in ocean heat content are linked with variations in surface warming. To investigate the forced response of ocean heat content (OHC) to anthropogenic aerosols (AA), we use an ensemble of historical simulations, which were carried out using a range of anthropogenic aerosol forcing magnitudes in a CMIP6-era global circulation model. We find that the centennial scale linear trends in historical ocean heat content are significantly sensitive to AA forcing magnitude ($-3.0\pm0.1$ x10$^{5}$ (J m$^{-3}$ century$^{-1}$)/(W m$^{-2}$), R$^2$=0.99), but interannual to multi-decadal variability in global ocean heat content appear largely independent of AA forcing magnitude. Comparison with observations find consistencies in different depth ranges and at different time scales with all but the strongest aerosol forcing magnitude, at least partly due to limited observational accuracy. We find broad negative sensitivity of ocean heat content to increased aerosol forcing magnitude across much of the tropics and sub-tropics. The polar regions and North Atlantic show the strongest heat content trends, and also show the strongest dependence on aerosol forcing magnitude. However, the ocean heat content response to increasing aerosol forcing magnitude in the North Atlantic and Southern Ocean is either dominated by internal variability, or strongly state dependent, showing different behaviour in different time periods. Our results suggest the response to aerosols in these regions is a complex combination of influences from ocean transport, atmospheric forcings, and sea ice responses.