Why are brake temperature limitations lower when the brake fans are running?
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)