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°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°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°C project slower shrinking than other models.