In that case, there's only so much hydraulic resistance in the circuit so you'll be running an extremely high flow rate. The pump will heat due to the loss of efficiency because of that high rate of flow.
BigInch's post details the fun unbounded heat rise until failure results!
We have a circuit which pumps liquid ethane into a pipeline. On this circuit is a minimum flow/maximum pressure controlling spillback, which goes to an accumulator on the suction of the pump.
If the pipeline shuts in, the recycle takes over, and we can see our pumpage temperatures rise quite quickly. There's no way to cool the pumpage, and there is only minor hydraulic loss in the system. Eventually, the ethane reaches a near vapor condition and the pumps vapor lock.
Of course, ethane is a different animal than water, but it still illustrates how fun recycle systems can be!