Most of the times it is not the "landing brake temp" bringing the problem, but the brake temp taxiing out.
I.e., a fairly empty Airbus taxiing behind a very slow taxiing 737 (some companies pay for blocktime!!) on a long taxiway (i.e. FRA rwy 18) involves quite a few brake actuations.
So reaching the takeoff position the brakes are reaching slowly their peak temp. Retracting the gear after takeoff, loosing the airflow, the temp is even getting higher. This requires to bring the gear down again, reduce speed with probable reconfiguratoin (slats) to observe gear overspeed limitation.
So, to avoid all the trouble, just let the gear down after takeoff for a while as a precautionary measure.
To keep the brake temp at max 100°C with help of the brake fan makes no sense from my point of view. 100°C is definitly not the optimum temperature for carbon brakes.
Thatīs at least what I am doing! (A-320 family)