Keep it simple.
If you never turned the fans on before departure the maximum brake temperature for take-off is 300 degrees.
If you did turn the fans on? The maximum brake temperature for take-off is 150 degrees.
Nick 1, in your scenario where the temperature is 250 degrees and the fans are on, you must leave the fans on until the temperature reaches 150 degrees, switch them off and then depart. If you had never switched the fans on the limit remains at 300 degrees, so you could depart immediately.
Why? The brake temperature sensors are located in a position immediately next to the flow of air from the fans. When the fans are running the air artificially "cools" the sensors so that they indicate a significantly lower temperature than the actual brake temperature. In reality, with the fans on, an indicated temperature of 150 degrees equates to a "real" brake temperature of 300 degrees.
Returning to the simple part of this;
1) Fans on? Keep them on until 150 degrees is indicated.
2) Fans off? 300 degrees is acceptable for take-off.