In the A320 FCOM it is stated that if the brake fans are running prior to takeoff then the brake temperature must be below 150 degrees Celsius. But if the brake fans are off then our limitation is 300 degrees Celsius. Any reason behind such different limits?
The fans cool not only the brakes, but also the temperature sensors, at different rates. The temperature difference is a measure to correct this anomaly. From the document Proper Operation of Carbon Brakes by Airbus Flight Operations Support:
... the temperature indicated in the cockpit when the brake fans are running is significantly lower than the temperature indicated when the brake fans are OFF. This is because the brake fans are ventilating the brake temperature sensor that is not located inside the material itself. Therefore, as soon as the brake fans are running, the indicated brake temperature decreases almost instantaneously.
... For all brake types, when the fans are running, the difference ranges typically from approximately 50°C at 100°C actual brake temperature up to about 150°C at 300°C actual brake temperature.
... When fans are selected, the warning will disappear instantaneously, but the takeoff must be delayed until the indicated temperature consistently decreases below 150°C (for a warning set at 300°C)