The subject of this post isn’t the only new research on how ocean heat content has changed. Zanna et al. have taken a new approach to estimating it based on sea surface temperature history.
Of course knowing sea surface temperature at some point in time, doesn’t tell you the ocean heat content profile throughout the depths of the ocean at that time. But if you know the sea surface temperature history, and the heat-content-at-depth history, you can (at least theoretically) find a “transfer function” which tells you how the heat content profile depends on the time history of surface temperature. After all, the waters at depth were near the surface some time in the past and that’s where and when they got their heat.