Marine heatwaves (MHWs) pose significant threats to Mediterranean marine ecosystems and coastal economies, and their frequency and severity are projected to increase under future climate change. In this context, coupled climate simulations are valuable tools to accurately characterize the properties of future MHWs in the Mediterranean. While Med-CORDEX fully-coupled Regional Climate System Models (RCSMs) offer enhanced resolution and improved representation of local processes relative to their parent Global Climate Models (GCMs), a systematic assessment of their added value for sea surface temperature (SST) and MHW properties has been lacking. This study quantifies the added value of Med-CORDEX RCSMs over the Mediterranean basin, evaluating their capacity to correct GCM biases and improve the spatiotemporal representation of SST and MHW probability distributions. Results show that added value is scale-dependent and metric-specific. RCSMs generally improve the SST spatial pattern and the shape and upper tail of its temporal distribution, but mostly fail to correct Mediterranean basin-averaged errors in the mean, standard deviation, 90th percentile and linear trend. For MHW duration, downscaling provides consistent and spatially widespread improvements across nearly all models, driven by a better representation of short-lived events. For MHW intensity, added value is model-dependent and not systematic: while the majority of RCSMs improve this metric, some models exhibit deterioration linked to model-specific features. These results demonstrate that higher horizontal resolution is a necessary but not sufficient condition for improved MHW representation, and that simultaneous advances in other model components are required to fully exploit the potential of regional downscaling.