The globally averaged diurnal temperature range (DTR) has shrunk since the mid-20th century, and climate models project further shrinking. Observations indicate a slowdown or reversal of this trend in recent decades. Here, we show that DTR has a minimum for average temperatures close to 0 degrees C. Observed DTR shrinks strongly at colder temperature, where warming shifts the average temperature toward the DTR minimum, and expands at warmer temperature, where warming shifts the average temperature away from the DTR minimum. Most, but not all climate models reproduce the minimum DTR close to average temperatures of 0 degrees C and a stronger DTR shrinking at colder temperature. In models that reproduce the DTR minimum, DTR shrinking slows down significantly in recent decades. Models project that the global-mean DTR will shrink over the 21st century, and models with a DTR minimum close to 0 degrees C project slower shrinking than other models. The diurnal temperature range, that is, the difference between daily maximum and minimum temperatures, affects both human health and plant development. Global data sets have shown a shrinking diurnal temperature range since the 1950s, but a recent study found that the diurnal temperature range had expanded again. In this study, we investigate how the diurnal temperature range behaves at different mean temperatures. We find that the diurnal temperature range is particularly small for temperatures close to the melting point of water (0 degrees C), and larger for both colder and warmer temperatures. Due to the latent heat of freezing/melting, more energy is required to warm the soil from -1 to +1 degrees C than from -3 to -1 degrees C or from 1 to 3 degrees C. The diurnal temperature range shrinks in regions and seasons with negative average temperature, where global warming pushes the average closer to 0 degrees C and expands for warmer temperature. Most, but not all climate models also show a narrow diurnal temperature range near 0 degrees C, shrinking of the temperature range at colder temperature and a slower reduction in the diurnal temperature range in recent decades. Models suggest that the currently observed expansion of the diurnal temperature range is a transient phenomenon. The diurnal temperature range (DTR) has a local minimum near average temperatures of 0 degrees C DTR in observations shrinks strongly for average temperatures below 0 degrees C and expands for warmer temperatures Climate models that reproduce the local DTR minimum near 0 degrees C show a significant slowdown of DTR shrinking in recent decades