It may not be the water pump but this is a bit strange and if the impeller isn't up to snuff this could happen. Never used to as this engine in it's basic format has been around for decades on end but somehow when they call a Chevy 350 a 5.7 something happens
BTW - the water pumps spins and pumps the whole time the engine is running - not just when the thermostat is open. When thermostat is closed, part open and wide open it still needs to circulate coolant inside the whole engine to keep it a uniform temp. Without thermostat the pump just pumps a too high % of it's ability right at the radiator without the mixing going on which is what the by-pass system is all about. Good luck,
T
Tom Greenleaf - MetroWest Boston - USA
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http://www.autoacsystems.com/tomgreenleaf/