Rapid changes in climatic conditions threaten both socioeconomic and ecological systems, as these might not be able to adapt or to migrate at the same pace as that of global warming. In particular, an increase of weather and climate extremes can lead to increased stress on human and natural systems, and a tendency for serious adverse effects. We rely on the EURO-CORDEX simulations and focus on the the screen-level daily mean temperature (T2m). We compare the shifting velocities of the cold and hot extremes with these of the associated central trends, i.e., the arithmetical mean or median. We define the extremes relative to the T2m distribution as it evolves with time over the period of 1951--2100. We find that temperature extremes shift at a similar velocity compared to that of the central trends. Accordingly, the T2m probability distribution shifts mostly as a whole, as the tails of the distribution increase together with the central trends. Exceptions occur however in specific regions and for the clustering of warm days, which shifts slower than all other extremes investigated in this study.