Abstract Atmosphere and ocean are coupled via air–sea interactions. The atmospheric conditions fuel the ocean circulation and its variability, but the extent to which ocean processes can affect the atmosphere at decadal time scales remains unclear. In particular, such low-frequency variability is difficult to extract from the short observational record, meaning that climate models are the primary tools deployed to resolve this question. Here, we assess how the ocean’s intrinsic variability leads to patterns of upper-ocean heat content that vary at decadal time scales. These patterns have the potential to feed back on the atmosphere and thereby affect climate modes of variability, such as El Niño or the interdecadal Pacific oscillation. We use the output from a global ocean–sea ice circulation model at three different horizontal resolutions, each driven by the same atmospheric reanalysis. To disentangle the variability of the ocean’s direct response to atmospheric forcing from the variability due to intrinsic ocean dynamics, we compare model runs driven with interannually varying forcing (1958–2018) and model runs driven with repeat-year forcing. Models with coarse resolution that rely on eddy parameterizations show (i) significantly reduced variance of the upper-ocean heat content at decadal time scales and (ii) differences in the spatial patterns of low-frequency variability compared with higher-resolution models. Climate projections are typically done with general circulation models with coarse-resolution ocean components. Therefore, these biases affect our ability to predict decadal climate modes of variability and, in turn, hinder climate projections. Our results suggest that for improving climate projections, the community should move toward coupled climate models with higher oceanic resolution.