How does the brain cool itself?
Computers rely on cooling mechanisms like heat sinks( an aluminum alloy mounted over the micro integrated chip) and fan. So far none of these mechanisms are utilized by nature, but analogies like cooling mechanisms in elephants which are in turn considered to be a model quite like the fan.
As the largest land animal, elephant's ears have crucial role in regulating homeostasis. When we see an elephant, it always wave its ears in order to reduce the brain temperature. On the other hand humming birds which are very smaller in size reduces its temperature by flowing blood to its wings. Humming birds wings flutter 90 times a second and it allows them to exchange much of its heat to the environment and the cooled blood is driven back to the brain.
The  carotid rete or rete mirabile in birds have been developed for heat exchange. In mammals, a pool of the cool venous
blood  returns from the nose or
head skin, exchanges the heat with
warm arterial blood of the carotid artery.
These arteries are sub divided into hundreds of
small arteries forming a net like structure which significantly improve the
heat transfer in brain.

Vascular retia mirabilia are also found in the limbs of a range of
mammals. These reduce the temperature in the extremities. Some of
these probably function to prevent heat loss in cold conditions by
reducing the temperature gradient between the limb and the
environment. Others reduce the temperature of the testes increasing
their productivity. In the neck of the dog, a rete mirabile protects
the brain when the body overheats during hunting; the venous blood is
cooled down by panting before entering the net.Reference


In Humans,

The net effect of heat production in the brain and brain cooling
keeps the brain cooler than the rest of the body and is achieved by
surrounding and bathing the brain with venous blood that has been
cooled outside the cranial vault, by bone and fat acting as
insulation, by the veins of the face and scalp through conduction,
convection, sweat and evaporation and by cooled venous blood flowing
through the cavernous and suboccipital cavernous sinuses cooling
incoming blood in the internal carotid and vertebral arteries before
it enters the brain. The combined effect of the brain cooling system
keeps the temperature inside the vault and brain about two to three
degrees cooler than the rest of the body. The effect is important
enough that some physical anthropologists attribute the extra-large
size of the human brain more to its exceptional cooling capacity than
to the increase in arterial blood flow that comes with upright
posture. Anthropologists refer to human encephalization due to
enhanced brain cooling capacity as the &quot;radiator theory&quot;.
Reference

Also yawning and panting are considered to be mechanisms to reduce brain temperature.