FCOM PRO-NOR-SOP-22 for IAE Engines:
Note: The flight crew should operate the engines at or near idle thrust for a cooling period of 3 min before engine shutdown, in order to thermally stabilize the engines. Idle reverse thrust and normal thrust to maneuver during taxi (i.e. at or near idle), are not considered as high thrust operations. Therefore, both of the following applies:
‐ If the flight crew uses idle reverse thrust for landing and normal thrust to maneuver during taxi after landing, the cooling period starts when the flight crew retards the thrust lever during the flare
‐ If the flight crew uses maximum reverse for landing, the cooling period starts when the flight crew sets the thrust lever to idle reverse during the landing rollout.
However, if operationally necessary, all engines can be shut down when the aircraft arrives at the gate, regardless of the time necessary for landing. Before engine shutdown, routine cooling periods that last less than the recommended time, can result in engine degradation.
CFM and NEO have a different guidance. Check the applicable FCOM in PRO-NOR-SOP-22