There have been decades, such as 2000-2009, when the observed globally averaged surface-temperature time series shows little increase or even a slightly negative trend (a hiatus period). However, the observed energy imbalance at the top-of-atmosphere for this recent decade indicates that a net energy flux into the climate system of about 1Wm-2 (refs , ) should be producing warming somewhere in the system. Here we analyse twenty-first-century climate-model simulations that maintain a consistent radiative imbalance at the top-of-atmosphere of about 1Wm-2 as observed for the past decade. Eight decades with a slightly negative global mean surface-temperature trend show that the ocean above 300m takes up significantly less heat whereas the ocean below 300m takes up significantly more, compared with non-hiatus decades. The model provides a plausible depiction of processes in the climate system causing the hiatus periods, and indicates that a hiatus period is a relatively common climate phenomenon and may be linked to La Niña-like conditions.