Estimating long-term modifications of the sea surface temperature (SST) is crucial for evaluating the current state of the oceans and to correctly assess the impact of climate change at regional scales. In this work, we analyze SST variations within the Mediterranean Sea and the adjacent Northeastern Atlantic box (west of the Strait of Gibraltar) over the last 37 years, by using a satellite-based dataset from the Copernicus Marine Environment Monitoring Service (CMEMS). We found a mean warming trend of 0.041 ± 0.006 ∘ C/year over the whole Mediterranean Sea from 1982 to 2018. The trend has an uneven spatial pattern, with values increasing from 0.036 ± 0.006 ∘ C/year in the western basin to 0.048 ± 0.006 ∘ C/year in the Levantine–Aegean basin. The Northeastern Atlantic box and the Mediterranean show a similar trend until the late 1990s. Afterwards, the Mediterranean SST continues to increase, whereas the Northeastern Atlantic box shows no significant trend, until ~2015. The observed change in the Mediterranean Sea affects not only the mean trend but also the amplitude of the Mediterranean seasonal signal, with consistent relative increase and decrease of summer and winter mean values, respectively, over the period considered. The analysis of SST changes occurred during the “satellite era” is further complemented by reconstructions also based on direct in situ SST measurements, i.e., the Extended Reconstructed SST (ERSST) and the Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST), which go back to the 19th century. The analysis of these longer time series, covering the last 165 years, indicates that the increasing Mediterranean trend, observed during the CMEMS operational period, is consistent with the Atlantic Multidecadal Oscillation (AMO), as it closely follows the last increasing period of AMO. This coincidence occurs at least until 2007, when the apparent onset of the decreasing phase of AMO is not seen in the Mediterranean SST evolution.