By the time the outbound blood reaches the hairpin turn it is as cold as the sea itself. By the time the in-bound blood reaches the interior of the whale, it is as warm as the interior. There is very little temperature gradient between the whale's surface and the sea, ergo, there is very little heat transfer, for a temperature gradient is needed to transfer heat. The whale's counter-current boundary system. The counter-current arrangement maintains a large heat gradient without the need for a heat pump such as is found in a refrigerator.
Energy is required to move the blood.
The countercurrent system will not work without motion in the blood stream. Of course, if the whale's heart stops beating, heat loss to its environment is the least of its problems. The blue heron standing in icy water keeps the heat from draining out of his body through his feet, in part, by standing on one foot, but also by the counter-current design of blood vessels in its other leg. The foot that is in the water is cold but heron's body remains warm. Engineers are familiar with this design and use it to maintain high temperatures inside boilers without having the boiler sides very hot and without much heat loss to the atmosphere surrounding the boiler.