The study of marine heat waves as extreme temperature events has a wide range of applications, from a gauge for ecological and socioeconomic impact to a climate change indicator. Various definitions of marine heat waves as extreme sea temperature events exist to account for its broad applicability, with statistical definitions based on percentile based thresholds being widespread in its use. Using satellite and model data of the Mediterranean Sea, we analyze the statistical implications of choosing baseline climatological periods for threshold delineation, which are either fixed in the past or shifted in time. We show that in the context of a warming Mediterranean Sea, using a fixed baseline leads to a saturation of marine heat wave days that compromises the significance of this marine indicator, with 90% of climate models analyzed predicting an average above 189 marine heat wave days per year by 2050 even for the lowest emission scenario. We argue that only with a moving baseline, can we reach a definition for marine heat waves which yield consistently rare extreme events.