Coolant flow

It sure is. That's why it's so important to have a radiator that can more than handle whatever you're trying to cool. Then the cooling system will work like it's supposed to. The thermostat will actually regulate temperature. If the radiator isn't up to the task, then the thermostat stays open all the time trying to "make up" for what the radiator lacks.
I might add that if any part of the cooling system isn't up to the task then the thermostat won't be able to regulate temperature.