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Abstract Marine heatwaves (MHWs)—extremely warm, persistent sea surface temperature (SST) anomalies causing substantial ecological and economic consequences—have increased worldwide in recent decades. Concurrent increases in global temperatures suggest that climate change impacted MHW occurrences, beyond random changes arising from natural internal variability. Moreover, the long-term SST warming trend was not constant but instead had more rapid warming in recent decades. Here we show that this nonlinear trend can—on its own—appear to increase SST variance and hence MHW frequency. Using a Linear Inverse Model to separate climate change contributions to SST means and internal variability, both in observations and CMIP6 historical simulations, we find that most MHW increases resulted from regional mean climate trends that alone increased the probability of SSTs exceeding a MHW threshold. Our results suggest the need to carefully attribute global warming-induced changes in climate extremes, which may not always reflect underlying changes in variability.