Take the radiator cap off. Start the car let it warm up so the thermostat opens up once it does you should be able to see the coolant circulating in there. If it's not then either the thermo is bad or the water pump is bad.
Another way to check is get the engine warmed up to operation temp. Then pop the hood and grab the upper radiator hose...pinch it shut..if you can feel pressure like it wanting to expand then the water pump is working. If you change Water Pump be sure and change your Timing Belt,Cam seals and front main seal as well. No reason in tearing it all apart and not do that. Doesn't make sense.
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