Ocean heat content (OHC) is a key climate variable that needs to be monitored to know how Earth's energy imbalance is changing, yet observing OHC remains a challenge. The present study examines whether a depth integral of the ocean's electrical conductivity (“conductance”), which may be inferred from both in situ methods and satellite magnetometers over the global ocean, could help monitor OHC. The ocean's electrical conductivity locally depends on temperature, salinity, and pressure, but it is not
as well known how the conductance depends on OHC and ocean salt content. By examining the output of an ocean state estimate shown to agree well with observations that have not been assimilated, this study evaluates the fundamental limitations of using perfectly known ocean conductance to predict OHC, rather than the challenges associated with accounting for observational error. It is found that the ocean's conductance and OHC fields are nonlinearly related but nevertheless highly correlated. A statistical framework tends to predict OHC more accurately than ocean salt content from ocean conductance in regions where conductivity is more sensitive to salinity than temperature. The annually (bidecadally) averaged OHC can be predicted from a combination of conductance and depth-averaged conductivity ocean fields to within nearly 0.1% (1%) error globally and even more accurately in many poorly observed (e.g., ice-covered) regions. Practical application of this statistical framework to monitor OHC requires examination of the effect of uncertainties in the observed bathymetry and ocean conductance, which vary with application.