Electricpete,
Good question.
My answer responds to the OP question of an "open loop" heat exchanger, but if you want to make it a real life situation then you close the loop with a radiator that is removing the same amount of total engine heat. In that case, as you know, a thermostat maintains control of the temperature entering the radiator, say 180 F, so the flow to the radiator and its temperature profile inside the radiator is independent of the fouling problem at the engine,which only causes the jacket Temperature to rise to accommodate the fouling. If you now increase the flow into the jacket, then the amount of increased flow rate would ends up bypassing the radiator,without affecting the flow through the radiator
So bottom line-- the exit temperature at the engine is always 180 and , of little consequence, but worth noting, owing to the increased flow, the entrance temperature to the jacket is somewhat increased because the delta T across the jacket is reduced.
Since.the maximum walll temperature is at the exit jacket wall where the water temperature is maximum.and at that point, you have q, the same flux I used previously, we can write
q=(Tw-180)/h
[BTW, we could have arrived at this without all the discussion following the the fsct that the water exits the engine at 180 F]
where h is proportional to V^.8 ; this leads to the obvious conclusion that the maximum wall temperature is reduced.
Seems that the actual closed loop case is easier to prove than the open loop.