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
Diabolo, I'm trying to connect the dots here - The JT8D on the 737-200 is a bypass engine (albeit low bypass ratio) and the clamshell reverser reverses both hot and cold flows.
And the high bypass engines I'm familiar with do not "simply cut the cold stream of air that cool the core and the casing" when in reverse.
Expand on what you're saying, please.