There are many places on the body to dissipate heat, and why the wrist? Why not the cooling headband or cooling fanny pack?
Skin is the reason.
Glabrous skin to be exact. Glabrous skin is non-hairy skin with specialized blood vessels that dissipate heat very efficiently. The vessels are close to the skin, and the heat from the blood can dissipate to the environment. The venous blood returning from these vascular in the hands, wrists, and feet circulate throughout the body.
The body only has a few areas with glabrous skin. So, if one was to choose a site to cool the body and restore homeostasis, the options are limited. Hands and feet have large patches of glabrous skin, but most daily activities require the use of the hands, the feet, or both. The next best candidates are the wrists and the ankles. Cooling can take place at these sites without disrupting manual or pedal activity. Of the two, the wrist has the more favorable anatomy. The bony prominences on either side of the ankle force any cooling device to be applied above that level. Unfortunately, glabrous skin turns into hairy skin not too far away from the foot. The underside (flexor side) of the wrist is an ideal spot for concentrated cooling. A cooling band can be firmly and comfortably attached to that area without interfering with hand or arm movements. Thus, when choosing a site with glabrous skin to take advantage of concentrated cooling, the underside of the wrist is optimal.