A control apparatus for controlling the overheat temperature of an evaporator of a refrigeration or heat pump system in which the evaporator, a compressor, a condenser and an expansion valve controllable by the control apparatus are arranged in series in a closed circuit, comprising: a monitoring means for monitoring the energy balance of the evaporator, the monitoring means including sensors for detecting the pressure and the temperature at the output of the evaporator or sensors for detecting the temperature at the input and at the output of the evaporator, an evaluating means for determining whether the refrigeration or heat pump system operates within a stable or unstable range of the evaporator based on the variables detected by the monitoring means, and a storage means in which the set value characteristics of the overheat temperature are stored, wherein the control apparatus approaches the respective value, by incremental reduction of the set value of the set value characteristics of the overheat temperature corresponding to the current operating point, to the stability limit of the refrigeration or heat pump system, when the evaluating means determines that the refrigeration or heat pump system operates within the unstable range of the evaporator, the control apparatus incrementally increases the set value of the overheat temperature until the evaluating means determines that the stable range of the evaporator has been reached again, and when the stable range of the evaporator has been reached again, the set value of the set value characteristics stored in the storage means for said operating point is overwritten by the current set value of the overheat temperature and is stored; characterized in that the evaluating means is set to form the gradient of the variation of the temperature detected in the monitoring means at the output of the evaporator, to determine an unstable condition of the evaporator of the refrigeration or heat pump system, when the gradient falls below a predetermined threshold α 1grenz, and to determine a stable condition of the evaporator of the refrigeration or heat pump system, when the gradient exceeds a predetermined threshold α 2grenz and for a predetermined interval lies between α 1grenz and α 2grenz. a monitoring means for monitoring the energy balance of the evaporator, the monitoring means including sensors for detecting the pressure and the temperature at the output of the evaporator or sensors for detecting the temperature at the input and at the output of the evaporator, an evaluating means for determining whether the refrigeration or heat pump system operates within a stable or unstable range of the evaporator based on the variables detected by the monitoring means, and a storage means in which the set value characteristics of the overheat temperature are stored, wherein the control apparatus approaches the respective value, by incremental reduction of the set value of the set value characteristics of the overheat temperature corresponding to the current operating point, to the stability limit of the refrigeration or heat pump system, when the evaluating means determines that the refrigeration or heat pump system operates within the unstable range of the evaporator, the control apparatus incrementally increases the set value of the overheat temperature until the evaluating means determines that the stable range of the evaporator has been reached again, and when the stable range of the evaporator has been reached again, the set value of the set value characteristics stored in the storage means for said operating point is overwritten by the current set value of the overheat temperature and is stored; characterized in that the evaluating means is set to form the gradient of the variation of the temperature detected in the monitoring means at the output of the evaporator, to determine an unstable condition of the evaporator of the refrigeration or heat pump system, when the gradient falls below a predetermined threshold α 1grenz, and to determine a stable condition of the evaporator of the refrigeration or heat pump system, when the gradient exceeds a predetermined threshold α 2grenz and for a predetermined interval lies between α 1grenz and α 2grenz.