In general, I think the study is interesting and the analysis robust. I have only two major concerns, one related to the data set used and the other more related to the motivations and implications of this work for the communities who might be interested (in particular Marine Protected Areas and aquaculture sector).

Motivation and Innovative aspects

Which are the main innovative aspects of this work with respect to the Marin et al. (2021) which focused on the coastal analysis and used an ensemble of different SST products? In their case motivations of the work were to provide an informative framework for coastal management since they focus on the analysis of coastal MHWs. In the present work the analysis has been extended to the whole Mediterranean. Apart from the scientific interest, what are the possible implications of this analysis for marine biodiversity and ecosystem functioning across various time scales and for marine economic activities at the regional scale? It would be nice if the authors could provide more clear motivations for this study at regional level (all the Mediterranean versus the coastal region) and the implications that their conclusions might have on adaptation measures at relevant time scales.

Methodology

Marin et al. 2021 found important differences between the SST products mainly for the MHW mean intensity, which was well correlated to SST variability, suggesting sensitivity of this metric to the specific SST data set. Indeed, one of their conclusion is that an ensemble approach should be adopted to minimize the impact of the choice of SST product on MHW metrics. Given that, according to your results, the interannual variability is the dominant driver only of the MHW mean intensity, how robust is your result since you use only one SST product which is also re-gridded from the original 0.05° resolution to a much coarser one? Can you comment on this?

Even if it is possible to find all the details of the SST product used here in the documentation that the authors refer to in Table 1, I think it would be useful for any reader to have a short summary of the main characteristics of the product given the possible sentivity of the results to the specificities of the SST satellite product.

Minor comments:

Line 99.

What do you mean exactly by “MHWs derived from both datasets are therefore relative to the initial state of the study period (1982)”?  

Lines 156-157

Our findings therefore indicate that, on top of the underlying mean warming, a large part of the western and central Mediterranean basin mainly experiences increased variability…

Fig.1c is not showing this. Most of the western Med shows decreased variability and in most of the central Med the trend of STD is not significant. I suggest that all the conclusions related to this statement should be revised.

Fig.2 shows the temporal evolution of all the different MHWs metrics, but not the linear trend (see Legend).

The legend of Fig.2 and Table 2 report twice the definition of the geographical areas.  

In general, the quality of the figures could be improved. In particular, the use of the same color bar but for different ranges of values in Fig.3 does not help an immediate interpretation.

General comments

In this manuscript, the authors explore sea surface temperature data to analyze long-term changes in MHW characteristics., distinguishing the mean warming and SST variability impacts. The study is interesting but the authors should better clarify the motivations of the study, as well as the  implications on marine ecosystems providing references. By comparing to the recent studies (cited by the authors), the novelty of the manuscript should be better highlighted. 

Specific comments

Introduction

L.28: reference in 2014 does not seem to me adequate when addressing the period 1982-2022, especially knowing the acceleration in global warming in the last decade and recent years. More recent publications: Martinez et al. (2023) 1982-2021, Juza et al. (2021)→ 1982-2020.

l. 30: I would suggest “warm oceanic events”

l. 30 replace “Marine Heatwaves (MHW)” by “marine heatwaves (MHWs)”

2.1 SST observations

The authors “re-gridded” the datasets to coarser resolution, for computational reasons. I do not understand such an exercise and degradation of the datasets.

The authors could provide a table or list of the derived datasets for clarity.

Are these datasets available in open access? It would be a real added value of the paper.

Maybe the authors could be interested by the paper from Amaya et al., 2023 Amaya 2023https://www.nature.com/articles/d41586-023-00924-2 

2.2 MHW analysis

l.78 “for a 5-day period” → add “at least” or “or more”

l.100: the authors want to directly compare their results to Marin et al. (2021). They will obviously find differences when using different periods…

l.105: I do not feel comfortable with the reference period 1982-2002, since it does not respect the 30-year period recommendation (Hobday et al., 2016).

l. 122-125: It could be great to provide some references. The choice of the metrics is driven by marine ecosystems implications. It should be clarified.

Trends: uncertainties are missing in the text. Could you precise which method is used and the level of significance?

Results

l. 189: “mean intensity seems to increase” → are they statistically increasing? or not?

l. 222: “forced by interannual variability”: what would be the results when distinguishing the seasons?

l.229: "opposing trend of the (reduced) variability → decreasing trend of the variability

Conclusions

l.284 "results potentially suggest”... A study over a more recent period could lead to different results. In particular, I think that the warming rate in WMED is higher than in EMED in the last decade… Have the two periods proposed in introduction/methodology been explored and analyzed to state such a conclusion?

l.290: I would delta “in most of the basin, mainly”

l.293: I would delete the parenthesis

l.303-305: see my previous comments concerning the seasons.

l.313-315: to be referred.

l.316-317: this statement has been repeated several times I think…

Figures

Figure 2: Could you define somewhere the boxes WMED, CMED, EMED? Maybe boxes could be added in Figure 1.

Figure 4 is not necessary