Changes in sub-daily precipitation extremes potentially lead to large impacts of climate change due to their influence on soil erosion, landslides, and flooding. However, these changes are still rather uncertain, with only limited high-resolution results available and a lack of fundamental knowledge on the processes leading to sub-daily extremes. Here, we study the response of hourly extremes in a convection-permitting regional climate model (CPRCM) for an idealized warming experiment—repeating present-day observed weather under warmer and moister conditions. Ten months of simulation covering summer and early autumn for two domains over western Central Europe and western Mediterranean are performed. In general, we obtain higher sensitivities to warming for local-scale extreme precipitation at the original grid-scale of 2.5–3 km than for aggregated analyses at a scale of 12–15 km, representative for currently conventional regional climate models. The grid-scale sensitivity over sea, and in particular over the Mediterranean Sea, approaches 12%–16% increase per degree, close to two times the Clausius–Clapeyron (CC) relation. In contrast, over the dry parts of Spain the sensitivity is close to the CC rate of 6%–7% per degree. For other land areas, sensitivities are in between these two values, with a tendency for the cooler and more humid areas to show lower scaling rates for the most intense hourly precipitation, whereas the land area surrounding the Mediterranean Sea shows the opposite behaviour with the largest increases projected for the most extreme hourly precipitation intensities. While our experimental setup only estimates the thermodynamic response of extremes due to moisture increases, and neglects a number of large-scale feedbacks that may temper future increases in precipitation extremes, some of the sensitivities reported here reflect findings from observational trends. Therefore, our results can provide guidance within which to understand recent observed trends and for future climate projections with CPRCMs.