The only area of the body yawning could have any kind of immediate cooling effect is the soft palate in the rear upper portion of the mouth—the part responsible

The only area of the body yawning could have any kind of immediate cooling effect is the soft palate in the rear upper portion of the mouth—the part responsible for brain freezes when eating ice cream. I don’t think ambient air passing over that palate would create a measurable change in brain temperature. Yawning always seemed, to me, to go hand in hand with stretching. I believe the reason we yawn is one in the same with the reason we stretch. By yawning, we are effectively stretching one of the few internal organs under our direct control: the lungs. It stretches the muscles involved in breathing, releasing trapped lactic acid built up over a long day of automated breathing. It improves blood oxygen concentration, which improves wakefulness and attention, which is exactly what you need when you are fatigued. Deep breathing also reduces anxiety, which is why breathwork is heavily incorporated in meditation. I think the contagious aspect could be an evolutionary behavior. Social mammals tend to work in groups, and “contagious” yawning was likely naturally selected for since all members of an exhausted group who yawn would be more awake and alert in the event of an attack or when hunting prey. These are physically strenuous (and tiring) activities that directly affect the survival of the organism.