From what i've learned in my Heat and Mass Transfer class in engineering...it really depends of several things mentioned somewhat above.
Heat flux (in Watts/Meter^2) = mass flow rate x specific heat x Difference in Temp
The mass flow rate is equal to = density x effective area x velocity.
So, in essence from those equations:
-If you increase the velocity OR the effective area (which area doesn't really apply so much here), you increase the mass flow rate.
-Increasing the mass flow rate in essence does increase the heat flux out of the system...so "yes" the greater the velocity of the fluid, the more it cools.
-But you also can have a greater heat flux out of the system by having a greater difference in temperatures. So the closer the temperatures of your fluid and say radiator are, you do in essence transfer less heat out of the system
Now...with that said, there ARE things besides that, that must be taken into account for the heat transfer. If you increase the velocity too much, you make the fluid too turbulent and risk superheating the fluid due to small air pockets created by eddy's (vortices basically) in the fluid.
So (as I've learned) it really comes down to a balance between velocity of the fluid, and making sure the fluid doesn't become overly turbulent causing you system to blow a hose