Cap does not effect operating temperature.
Low air flow at idle/low speeds,coolant moving too fast through the radiator is the problem.
The temperature will always rise at the sensor when engine is shut down.
It it is not going above 200,that is not a problem.
Was the water pump replaced and with what?
No, but a too low pressure cap or one leaking/ other can allow hot spots to explode into boiling pockets, and encourage unwanted overflow both running, and especially on shutdown
