When in doubt, cooling the brain always seems like a good answer:
"Based on the brain cooling hypothesis, we suggest that there should be a thermal window in which yawning should occur," Gallup said. "For instance, yawning should not occur when ambient temperatures exceed body temperature, as taking a deep inhalation of warm air would be counterproductive. In addition, yawning when it is extremely cold may be maladaptive, as this may send unusually cold air to the brain, which may produce a thermal shock."
The parakeets yawned as predicted.
It's now believed yawning operates like a radiator for birds and mammals.
Well, I don’t know if the brain in particular is cooled by a yawn; we’re really talking about core temperature. Since this is more or less set in the hypothalamus, we might say that the local temperature in the brain causes yawning, which lowers the body’s temperature. Which I assume would be in the research paper.
But I have to tell you I’m yawning like crazy just writing this post.