If its an electric water pump, and is not connected to the bypass tube coming out of the intake manifold, and there are no holes in the thermostat to allow water circulation, the pump is just cavitating and not moving any water. If it is connected to the bypass tube coming out of the intake manifold, then it is circulating water through the engine, but not through the radiator. A mechanical pump will usually be connected to the bypass tube, so it will be circulating water through the engine until the thermostat opens, at which point it begins circulating water through the radiator.