If you're not pushing water through the radiator and the pump is good, the pump is probably cavitating and is spinning in what is essentially an air pocket. You could slow the pump down with a pulley change or go to a pump with a different impeller design. You can also add a product like Water Wetter that is a surfactant that lowers the surface tension of the water, ie making it slipperier and reducing the tendency to cavitate.
Don't know what you're using for coolant, but during the summer, I use only water, Water Wetter and Zerex water pump lubricant and anti-corrosion treatment and also added a bung to the radiator to screw in a zinc anode (I get from the boat supply store -- also a good source for stainless fasteners and high-grade electrical components) to reduce corrosion. You have to run anti-freeze in the winter, but anti-freeze reduces the efficiency of the coolant