So, yes - this is true...
But, it's diminishing returns... doubling the flow rate does not double the heat transfer. It increases, but doesn't double. In addition, to double the flow rate requires a lot more pressure - ~4x so it's difficult to double the flow rate inside the cowl without modifying the fins. Modifying the fins (reducing restriction - bigger gaps or less fins) would drastically reduce the heat transfer.
Slower flow rates result in the fluid being closer to the stove temperature, but cannot remove near as much heat.