If no reverser had been selected during Rollout or even at Idle power you do not need cooldown.
Reason, on Bypass Engine cold stream reverser you simply cut the cold stream of air that cool the core and the casing of the engine. After reverser check your EGT and you will notice that Ground Idle EGT values are greater that normal.
737-200 did not required cooldown after landing. Hot stream thrust reverser installations. Correct me if I am wrong
Sincerely