The content of this dataset includes (a) observed product, which is the averaged product of the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST), the Extended Reconstructed Sea Surface Temperature version 5 (ERSSTv5), and the Centennial in situ Observation-Based Estimates (COBE). This is called "global_sst_1958to2017.mat", i.e., 60 yrs of monthly SST over 1958-2017; it also contains the trend, the seasonal climatology, the anomaly field after subtracting trend and seasonal climatology, longitude, latitude, time, and land-sea mask. (b) 20 realizations of long SST simulation generated by a Linear Inverse Model (LIM). Each realization contains 6000 months (or 500 yrs) of SST. The file is named "stochastic_simulation_lim_sst_mem*.mat". To cite dataset if plot or extracted used in any publication, use the reference below: Xu, T., et al. (2022). "An increase in marine heatwaves without significant changes in surface ocean temperature variability." Nature Communications 13(1): 7396.