Many years ago I had a car which got a cracked block evidently from putting
cold water into an overheated engine. Ever since, I have been concerned about
putting cold water into a warm engine.

If you start with a cold car, drain the radiator and open the block plugs to
get most of the anti-freeze/water out, then refill with cold water containing a
flushing compound. there's nothing to be concerned about. But if you run the
car for half an hour then drain it out again, according to directions, is it
dangerous to then put in the new antifreeze and cold water? Or, is it a problem
only when the engine has been overheated, for example from a lack of coolant.

If you have this done professionally, they don't seem to worry about draining
and filling a car which has just been brought in off the road.

Any guidance on this would be appreciated.