If the water pump, cooling passages, and thermostat (if it exists for your model) are clear and working as expected, you are having an overheat situation still occurring if the temp sensor is working correctly.
On a Fuel injected outboard, especially 4 stroke motor, that motor and the heads are probably running warmer than versus running a 2 stroke carbed motor.
They run warm/hotter because of the tight tolerances to conserve fuel on fuel injection motors, that and Ethanol based fuel does increase the temperature which gas burns.
It's possible that the motor may be having difficulty shedding heat when quickly going from fast to idle speed.
There are too many factors to just spitball likely causes, especially if no engine codes are produced.
What the boat motor needs is a skilled professional with the diagnostic software to run it on the lake, dyno, or test tank it while using an infrared temp gun to find out why it is overheating so easily from high rpms to idle.
If there are no codes or obvious tell-tale signs in the real time dignostic software, I would be focusing on a mechanical issue or cooling issue by using the IR temp gun on the cylinders.
