Extreme convective precipitation is expected to increase with global warming. However, the rate of increase and the understanding of contributing processes remain highly uncertain. We investigated characteristics of convective rain cells like area, intensity, and lifetime as simulated by a convection‐permitting climate model in the area of Germany under historical (1976–2005) and future (end‐of‐century, RCP8.5 scenario) conditions. To this end, a tracking algorithm was applied to 5‐min precipitation output. While the number of convective cells is virtually similar under historical and future conditions, there are more intense and larger cells in the future. This yields an increase in hourly precipitation extremes, although mean precipitation decreases. The relative change in the frequency distributions of area, intensity, and precipitation sum per cell is highest for the most extreme percentiles, suggesting that extreme events intensify the most. Furthermore, we investigated the temperature and moisture scaling of cell characteristics. The temperature scaling drops off at high temperatures, with a shift in drop‐off towards higher temperatures in the future, allowing for higher peak values. In contrast, dew point temperature scaling shows consistent rates across the whole dew point range. Cell characteristics scale at varying rates, either below (mean intensity), at about (maximum intensity and area), or above (precipitation sum) the Clausius–Clapeyron rate. Thus, the widely investigated extreme precipitation scaling at fixed locations is a complex product of the scaling of different cell characteristics. The dew point scaling rates and absolute values of the scaling curves in historical and future conditions are closest for the highest percentiles. Therefore, near‐surface humidity provides a good predictor for the upper limit of for example, maximum intensity and total precipitation of individual convective cells. However, the frequency distribution of the number of cells depending on dew point temperature changes in the future, preventing statistical inference of extreme precipitation from near‐surface humidity.We investigated characteristics of convective rain cells under historical and future conditions in convection‐permitting climate simulations using a tracking algorithm. There are more intense and larger cells in the future yielding an increase in hourly precipitation extremes. The temperature scaling curves of cell characteristics shift towards higher peak values at higher temperatures in the future. In contrast, cell characteristics scale consistently with dew point temperature. Therefore, near‐surface humidity provides a good predictor for the upper limit of for example, maximum intensity, and total precipitation of convective cells