CV, perhaps my point wasn't clear enough.
The brake pack could be hot from previous landings.
With cooling, the taxi / takeoff limits would be respected.
During the cooling there would be some heat flow from the pack into the tyres; without tyre temp measurement, limits have to be deduced from brake temp, cooling time, and possibly previous flights.
Thus the taxi / takeoff temps could be within limits, but the brakes should be further cooled after take off to minimise heat flow, heat build up in the tyres, in the wheel bay.