Your question is a great one. Often much confusion about water systems. Lucas has the good answer. Though I have not done calculations, and probably won't...a simple electric pump that can handle both 230 degrees F, (110 C) and about 15 psi. system pressure. (1.03 bar) Cooling here is all about proper residence time...in the radiator, but really? Fancy calculations is my life and a great waste of time here.
Ryan and Lucas have parts of the answer. Our engines will produce some fairly high temperatures. Sorry, I do not have cylinder or good head temps,(230 degrees at the head?) but do have exhaust gas temps.
What is important to know about water cooling is that you do NOT need high flow, but do need variable flow. It is more important to understand heat removal. Of course, actual data is priceless, but you can infer much from existing bikes and parts.
The radiator you have is probably bigger than required, though that does not mean it will not work. The Malossi 12V pump is near perfect for the job. Designed for the Pressure and temperature profile already...and low battery draw. Mount it to draw liquids from the coolest point of the radiator...at the bottom outlet. Keeps it cooler and consistently working with the highest possible suction pressure.
Note that it is a centrifugal pump, which is the right design for the system. The 12V water pumps designed for motorhomes water systems is a sketchy and potentially problematic design. They are "pulse pumps", meaning near positive displacement. Often diaphragm or wobble plate or similar. They last a long time pumping water...probably the right flow regime, but that is it. The drawbacks are simple: Noisy...maybe designed to handle high temperatures, maybe not? They cannot handle being dead-headed, so need an auto shutoff. Mind you, the same design is used in cars and diesels as a lift pump, but again, must have a shutoff switch. My '01 Dodge Cummins ate them up! Not from the temperature in this case, but from the variable pressures...engine needs/fuel liquid head pressure...high pressure pump demand. Cheap though? Buy one at any RV supply.
You also must ensure that your flow routing is up flow on the engine side...coolest water in the bottom, from the bottom of the radiator, hottest out the top, through the thermostat to the radiator inlet at the top. What is not commonly known is that radiators, besides being many sizes, thicknesses and number of core rows, work best if the flow is cross flow. meaning side to side. Top of hot inlet, up and down and up and down....until the flow reaches the bottom outlet. Some dirt bike radiators or simply top to bottom, or have two...the bottom of the first feeds the top of the second. Cross flow works.
Most importantly, consider the use of your scooter. A drag race scooter is one and done! Shit and git! They very likely do not have a thermostat. Just enough cooling to be on the edge of holing a piston.
You will need a thermostat! It is the thing that will allow your other components to work properly. There are in-line thermostats, get one. Mount is near the cylinder head outlet. If you chose to monitor temperature on the water side, do it after the head, but before the thermostat. My belief is that you should know what the engine is doing, not how well the thermostat is performing. Further, it tells you if your overall cooling is adequate. ( I monitor exhaust gas temps, cooling water and cylinder head. Maybe just so I know what to tear down first when I blow it up.)
The low pressure pumps are simple and easy, but centrifugal pumps can withstand no flow, (Thermostat closed) for short periods. That is why all cars and bikes use centrifugal pumps. What causes the wear at the pump face is a few things, but the two common causes are dirty system liquids and cavitation, (intermittent flow)...not no flow.
In other words, you can have a real big radiator and still have it do its job. Too big and the thermostat stays closed longer, potentially causing large temperature swings, which can cause both performance changes and premature failures from metal fatigue.
So you need a design with:
* Down or cross flow Radiator
*Thermostat
*12V pump
*Proper hose routing
*Fan
*Overflow bottle (If you overpressure one time...you'll know why!)
The use of a fan is actually somewhat optional, however it is cheap and easy protection. If your radiator is oversized, the fan may never come on...(I know people who prefer this to eliminate a fan, but select a thermostat temp. and hope for the best)...undersized and it never shuts off.
I have a fan that is switch mounted...only used for extreme duty on my air cooled engine. If you put one on a water cooler, make it temperature controlled. This one from Trail Tech, has a built in display! Cheap, good looking and functional.
I use expensive silicon hoses, but just because they look good...no debate over function needed. I do not believe that they "perform better" than rubber in thermal terms. IT is a good argument, if you're pumping bazillion rpm's/hp, what ever. Not sure if measurable in our systems, even if 95cc conversions. But again...they look cool!
