We analyse a large number of multi-century pre-industrial control simulations from the fifth phase of the Coupled Model Intercomparison Project (CMIP5) to investigate relationships between: net top-of-atmosphere radiation (TOA), globally averaged surface temperature (GST), and globally integrated ocean heat content (OHC) on decadal timescales. Consistent with previous studies, we find that large trends (~0.3 K dec−1) in GST can arise from internal climate variability and that these trends are generally an unreliable indicator of TOA over the same period. In contrast, trends in total OHC explain 95% or more of the variance in TOA for two-thirds of the models analysed; emphasizing the oceans' role as Earth's primary energy store. Correlation of trends in total system energy (TE ≡ time integrated TOA) against trends in OHC suggests that for most models the ocean becomes the dominant term in the planetary energy budget on a timescale of about 12 months. In the context of the recent pause in global surface temperature rise, we investigate the potential importance of internal climate variability in both TOA and ocean heat rearrangement. The model simulations suggest that both factors can account for O (0.1 W m−2) on decadal timescales and may play an important role in the recently observed trends in GST and 0–700 m (and 0–1800 m) ocean heat uptake.