A new approach to monitor ocean heat content (OHC) is proposed to overcome challenges with observing OHC over the entire ocean. The output of an ocean state estimate (ECCO) is sampled along historical hydrographic transects, a machine learning algorithm (GAM) is trained on these samples, and OHC is estimated everywhere using information inferable from various global satellite coverage. Assuming the ECCO output is perfect observational data, a GAM can estimate OHC within 0.15% spatial root-mean-square error (RMSE). This RMSE is sensitive to the spatial variance in OHC that gets sampled by hydrographic transects, the variables included in the GAM, and their measurement errors when inferred from satellite data. OHC could be remotely monitored over sufficiently long time scales when enough spatial variance in OHC is explained in the training data over those time scales.