The study presents a time-dependent analysis of threats from man-made climate change at 244 UNESCO cultural and natural heritage sites in the Mediterranean. The hazards in our research are estimated by indices based on extremes of heat, fire weather conditions, heavy rainfall days, frost days, changes in mean sea level and aridity at each site. These indices were calculated from regional EUROCORDEX simulations, cover the period 1971–2100 and refer to two IPCC emission scenarios, namely RCP4.5 and RCP8.5. A combined threat index was next calculated, as explained in the text, together with its synergy with local exposure geophysical threats, such as seismicity, topography and proximity to forests and seas. All indices related to man-made climate change show an overall increasing trend from present to the end of the twenty-first century. Some of these increasing trends are intensified after the 2030s and 2040s, except for the case of the days with frost. As the global warming evolves, in both IPCC scenarios studied, the combined threat to the majority of UNESCO sites studied increases. Notable is the amplification of the threat at sites vulnerable to seismic activity and to other local or regional topography and geophysical regional characteristics. Our conclusion is that the majority of heritage sites in the Mediterranean are vulnerable to an increasing rate of threats from man-made global warming and extreme events. Seismic activity is magnifying these threats only at the sites in which that additional hazard applies. Based on the proposed combined threat index, for the worst-case scenario (RCP8.5) 35 monument sites fall within the “high hazard” and 12 sites fall under the category “extreme hazard”.