We use control run data from three Met Office Hadley Centre climate models to investigate the relationship between: net top-of-atmosphere radiation balance (TOA), globally averaged sea surface temperature (SST); and globally averaged ocean heat content (OHC) on decadal timescales. All three models show substantial decadal variability in SST, which could easily mask the long-term warming associated with anthropogenic climate change over a decade. Regression analyses are used to estimate the uncertainty of TOA, given the trend in SST or OHC over the same period. We show that decadal trends in SST are only weakly indicative of changes in TOA. Trends in total OHC strongly constrain TOA, since the ocean is the primary heat store in the Earth System. Integrating OHC over increasing model levels, provides an increasingly good indication of TOA changes. To achieve a given accuracy in TOA estimated from OHC we find that there is a trade-off between measuring for longer or deeper. Our model results suggest that there is potential for substantial improvement in our ability to monitor Earth's radiation balance by more comprehensive observation of the global ocean.