So a normal car radiator just has a strip of copper tubing that is folded accordion-style from the top left to the bottom right. Air flows over the copper perpendicular (at a right angle) to the flow of coolant. The reason this makes a radiator super–inefficient is because the farther the coolant gets, the less the gradient between coolant and air.
The air near the top right of the radiator is the only patch of air that gets the hottest dose; as the coolant moves down the line, it is already cooled some, so it has less heat to give to more air that it encounters.
A gill, on the other hand, is extremely efficient at maximizing the oxygen concentration in its blood. In principle we could redesign a radiator like a gill, maximizing the heat concentration instead of oxygen. In a gill, blood flows opposite to the flow of water. As the water comes in, it meets blood that already has super high concentration of oxygen, but the further it goes the more oxygen-deprived the blood is and the more the water will give it. At the back end of the gill, blood and water are completely deprived of oxygen, because it is all taken from the blood at the front of the gill. This dramatic separation of concentration is easily accomplished because of countercurrent exchange, which I have just described.
I have already done several CAD drawings of how the radiator design might look. There are a few little differences from a gill, but I believe it is a much better system.