If your T stat is working correctly I do not believe the water could be moving through the radiator too fast. The T stat controls the flow but opening and closing based on temp in an effort to regulate the system.
So if you take this in simple form, there are 2 things at work here;
1. the engine is producing heat through the ignition of air/fuel and the friction of the various moving parts.
2. the cooling system is moving fluid through the engine via the water jackets which is absorbing the heat generated by the engine and once the temp reaches the threshold of the thermostat is released into the radiator where it transfers the heat to the radiator which is cooled by the passing air flowing through it, thus cooling the fluid as it returns to the system to repeat this cycle. (overly simplified but I think generally accurate).
So, this then leaves us to deal with both sides; making the heat and removing the heat. Since we all want our engines to run as good as they can, there are limited things we can do to reduce the amount of heat produced, however it should be noted that timing can and does have a direct effect on this effect. Secondary to this can be the removal of ambient heat residing in the engine bay but in a street car not a lot can be done here short of wrapping the exhaust and/or creating openings for the heat to exit which most will not want to do. Therefore, adjustment of the timing is the one thing that can be done that has a direct effect on the reduction of heat produced.
This then leaves the issue of cooling and how to deal with that. In a perfect world, the thermostat will regulate the heat by opening and closing, however if the engine produces more heat than the cooling system can remove, the T stat will just remain open all the time and so long as the temps don't climb this isn't an issue. However if the temps do climb and continue say past 220, then of course there can be problems. Your cooling system has to be set up to support the amount of heat produced (some rate it by HP but I believe this to be anecdotal and an attempt to provide some level of understanding of the process).
There is a lot of "voodoo" surrounding cooling systems but it really comes down to volume, fluid flow, air flow and surface contact area. You have to have enough flow so that the fluid is moving in large enough quantities to absorb enough of the heat and move it to the radiator. Your system has to be big enough to able to present enough volume so that a portion can be cooled as another part is heated. You have to be able to move enough air across the radiator to extract/remove enough heat to reduce the temperature significantly in order to repeat and sustain the system. Lastly but in conjunction with the air flow is that you have to have enough surface contact area in the radiator for the air flow to contact and remove heat.
I will say up front that there is a seemingly huge amount of "black magic" too aftermarket cooling systems and accessories, thus it is very difficult to nail down what will work for any particular application and situation. Perhaps, the biggest issue is that there are so many variable ranging from application to environment and it is almost impossible for manufacturers to provide exacting details on what will work. Therefore we are left with general concepts such as "run the biggest radiator possible" and "use high CFM fans".
Simply put, a large 3 core radiator with a proper fan and shroud with a good thermostat should cool most engines adequately. The problem here is that all of these have their own variables. A high flow pump will definitely help most cases and I am very skeptical that it could be moving the water/fluid "too fast".
Have you tried "Water Wetter"? Perhaps this will solve your issues?
