need to test the car extensively after radiator replacement and coolant top up, as u mentioned that engine heat up sign appeared on the way to dealership.
i know very well about G series engines, which are almost bullet proof, a couple of heat ups wont harm them at all.
but these modern, a bit complex and high compression engines have very small clearances so heat up might harm them more.
atleast change engine oil before starting/testing the engine.
i hope dealership will make sure that engine health is perfect without any doubt