Once the engine reaches its normal operating temperature, and you're not spending a lot of time idling, it shouldn't get much hotter. Assuming you have an air cooled engine the air moving over the cylinder and head is the way it dissipates heat. Even prolonged running should not increase the engine temperature significantly.
This is especially true with a 2 cycle engine that gets its lubrication from the oil mixed with the fuel. By comparason, a 4 stroke engine with oil in a crankcase can see some loss of lubrication due to the breakdown of oil at high temperature. This would not be a factor with modern oil in a motorized bicycle however because you're never going to run it far or long enough to see any appreciable oil degradation between oil changes.
There really is no advantage to a "cool down" period other than to give your butt a break