semi technical to Dave of Mystic
I agree that the thermostat (and waterpump) keep the exit coolant temperature at about the same temperature whether at load or idling. You have to look closer at the operating engine to see the reason for the mfg recommendation. An engine running at load has many times the heat transferred to the coolant as compared to an idling engine and the temperature gradient is much steeper and absolute temperature values in the head from combustion chamber surface to water jacket surface are much higher at load than at idle. Thus, if the engine is cut off suddenly from load condition, the local heat in the engine head adjacent to the combustion chamber will continue to be transferred to the coolant, but since the coolant is no longer circulating, can locally overheat. I demonstrated this by accident early in my ownership of a raw water cooled 2gm yanmar. If the engine is shut down suddenly after say running at 2800 rpm for a five or ten minutes or more and then restarted after only a few minutes, it screeches the high temperature alarm until enough water has circulated through the engine to bring the coolant temperature down at the location of the temperature sensor. Unnerving, especially until I figured out what was going on. Better follow manufacturer's recommendationI have a John Deere tractor also with a Yanmar engine and the manufacturer's recommendation for idling before shutdown is the same. Probably any engine that operates high on the power curve should be idled before shutdown.