okay, two things:
1) whenever engine is hot, never remove the radiator cap, it's not worth the risk ...the boiling water can literally burn anything it touches, your hands face, etc...
2) and the chances that you have a water hose near you when your car heats up are less than 2% : ) 98 percent of the time it would heat up in the middle of the road (not at one's house when the car is parked) so even if you have water bottle in the car it would not be enough to waste on a hot engine because as soon as cold water touches a hot running engine, a large amount of it would evaporate, and the remaining amount that would go in the radiator could cause the engine block to crack due to the sudden change in temperature.
therefore, in my opinion, the best way is to shut the engine off, let it cool down to normal temperature, then pour water inside the radiator.
i am not sure how can an engine while running be cooled down ?
as it would continuously produce heat and there's excessive chance of engine seizure or blown head gasket ..