But no one has answered WHY.
Startup: The casing is lightweight, but the rotor(s) very massive by comparison. The casing thus heats up and grows in diameter in a minute or so while the rotor takes much longer. During this stabilization interval the seal clearances, blade tip clearances, and axial clearances are out of whack, causing a temporary inefficiency in the engine operating cycle.
If takeoff throttle is applied in this condition, temperatures will be higher than normal because of this inefficiency. An extra few minutes at low power saves wear and tear on the engine.
Shutdown: If the rotor is still hot while the casing is rapidly cooled, there is risk of a rub. A couple of RJ pilots experienced this at FL410 a year ago with sad results (search for "core lock")
Hope this helps.