To learn more about how while the observed sea surface temperature (SST) is rising at midlatitudes, the concurrent ocean record shows that stratification is not unequivocally increasing nor is MLD shoaling, check out this paper:

The warmer the ocean surface, the shallower the mixed layer. How much of this is true?

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For the first time and against all expectations, this study shows that surface warming is not definitively linked to a more stratified and less mixed ocean, according to three midlatitudes study areas. Thus, it reveals that subtle interplay between changes in circulation and atmospheric forcing contribute to find warmer and deeper mixed layer depth (MLDs).