In our cars once it'* started the water pump being belt driven circulates coolant. With the thermostat in what we call the closed position, it'* certainly not a much flow. There is flow though.
Was some work done on the car recently prior to the overheating issue? Sometimes an air bubble can develop in the system that is tough to get past. Many people fil through the thermostat hole before putting it in and sealing it up.
Some other ideas could be a plugged heater core or plugged radiator. Have you tried flushing water through the cooling system with only hose pressure and found it to flow through?
00 Regal GS: All kinds of cool stuff.