Anomalous warming of the upper ocean is increasingly being observed in the Mediterranean Sea. Extreme events, known as marine heatwaves (MHWs), can have a profound impact on marine ecosystems, and their correct detection and characterization are crucial to define future impact scenarios. Here, we analyze MHWs observed over the last 41 years (1982-2022) in the Mediterranean sea surface temperatures (SSTs). We show that the intensification in frequency, intensity, and duration of Mediterranean MHWs in recent years is mainly due to a shift in SST mean that occurred in the last two decades and largely reduced when analyzing detrended SST data. Detrending thus allows the use of a fixed climatology without overestimating MHW properties over time and distinguishes long-term warming (i.e., trend) from transient and abrupt SST changes. Analogous results are also found over a shorter temporal period, by analyzing 13 years (2007-2020) of in situ data collected at different depths (5 to 40 m) at Columbretes Islands. Additionally, the in situ analysis reveals that atmospheric summer heatwaves could affect a layer of 10 m in depth. Lastly, a catalogue of the major Mediterranean MHWs that have occurred since 1982 is presented. This catalogue evidences an exceptionally long-lasting and intense MHW, starting in May 2022 and persisting, at least, until the end of the year, resulting in the event with the highest cumulative intensity just after the well-known 2003 MHW event.