I can see it's time to break out some heat transfer discussions when people continue to say the thermostat is required to slow the coolant flow in a radiator "to have enough time to transfer heat". Absolutely false!
The addition of a thermostat, besides getting an engine up to an optimal operating temperature, will add marginal coolant back pressure in the engine and add turbulence to the coolant flow. The marginal pressure increase will hold the coolant in the liquid state at a slightly higher temperature thereby helping to reduce the potential creation of steam pockets internal to the engine. Turbulent flow is more efficient at heat transfer than laminar flow. Therefore, any turbulence added by the thermostat can improve the heat transfer efficiency of the radiator. So, if someone tells you they had an overheating problem and solved it by adding a thermostat, they added turbulence to the coolant entering the radiator which in fact did improve their cooling system.
As far as flow goes, increased flow in a closed loop cooling system improves the system efficiency (not degrades it). Here's the fallacy in the flow argument: If increasing the flow degraded the heat rejection in the radiator, then it would also follow that the heat absorption in the water jackets would also be degraded. Therefore, the coolant would in fact absorb less heat and actually be cooler. The engine block would get hotter, the combustion chamber temperatures would increase and exhaust gas temperatures would increase. But the engine would appear to run cooler from a coolant standpoint. In fact it doesn't work that way in a closed loop system, increasing the flow improves the heat transfer process.
The net time the coolant spends in the radiator remains the same in a closed system, regardless of flow rates (assuming everything else is equal). Don't believe it? Try this... Let's consider a flow rate where the time through the radiator is 10 seconds. Now let's double the flow rate. It makes sense that the coolant must flow through the radiator twice as fast which equals 5 seconds. Now...since the flow rate is double, the coolant must flow through the radiator 2 times at this rate versus only once at the slower rate. Therefore the coolant makes two trips through the radiator at 5 seconds per trip. This results in the same length of time of 10 seconds.