Mmm.. the heat output of an internal combustion engine is pretty much directly related to the rate of combustion == engine RPM for the most part.

My car generally varies between 1000 RPM at idle to 3000 RPM at highway speed. The water pump is therefore most needed at 3000 RPM, where it just happens to run three times as fast as at 1000 RPM! On a hot summer day, the airflow around the engine doesn't have nearly the cooling impact of the water pump (and radiator etc..), so I don't see any need to control the pump separately from engine RPM.

Until winter arrives, that is. Many days in the winter here it would be nice to have the water pump run at a much lower rate for the first half hour or so of operation. But not really, because that same water is used to heat the interior of the car, and if it circulated less, we'd freeze our butts off (well, not me.. my Subaru has electrically heated front seats!).

As for turning off the pump during engine warm up, I dunno. Most all cars have a theromostat valve to keep water from circulating outside of the engine block until it has warmed up to a certain temperature, so the pump isn't really slowing down engine warm up there. More like just evenly distributing heat around the engine block instead, so it doesn't crack open from intensely concentrated heat around the combustion chambers.

Cheers