Thermal hysteresis is used in reference to a difference between freezing temperature and melting temperature, as is the condition for pure water, which melts at close to 0°C, but will supercool to about −42°C in bulk (and even further on surfaces) when no nucleators are present[1]. When nucleators are present (such as bacterial nucleating proteins) the melting point and the freezing point of water are nearly the same, and there is no thermal hysteresis[2]. When nucleators are present with antifreeze proteins, the freezing point is depressed below the melting point, restoring thermal hysteresis.
More precisely, thermal hysteresis describes the condition where thermal history determines the behavior and properties of the system, as happens between the freezing temperature and melting temperature of water, when the temperatures are different. Warming between the two temperatures and cooling between the two temperatures will have different effects, depending on the thermal history, rather than simply on the temperature.