The global warming hiatus during the first decade of the 21st century has posed a challenge to the scientific community, though a leading explanation is that it was caused by internal variability overlaying a forced global warming trend. Here, we apply the Winton-Held two-layer model and show that the probability of the observed 2000–2012 hiatus period to arise from internal variability driven by white noise is larger if climate sensitivity is low. This is due to the delayed response of the oceans that cause the forced trend to increase faster with rising climate sensitivity than does natural variability, leading to a decreasing likelihood of observing the hiatus. The results are confirmed with the latest climate models participating in the Coupled Model Intercomparison Project (CMIP6).