Marine heat waves affect ocean ecosystems and are expected to become more frequent and intense. Earth system models’ ability to reproduce extreme ocean temperature statistics has not been tested quantitatively, making the reliability of their future projections of marine heat waves uncertain. We demonstrate that annual maxima of detrended anomalies in daily mean sea surface temperatures (SSTs) over 39 years of global satellite observations are described excellently by the generalized extreme value distribution. If models can reproduce the observed distribution of SST extremes, this increases confidence in their marine heat wave projections. 14 CMIP6 models' historical realizations reproduce the satellite-based distribution and its parameters’ spatial patterns. We find that maximum ocean temperatures will become warmer (by 1.07° ± 0.17°C under 2°C warming and 2.04° ± 0.18°C under 3.2°C warming). These changes are mainly due to mean SST increases, slightly reinforced by SST seasonality increases. Our study quantifies ocean temperature extremes and gives confidence to model projections of marine heat waves.