In their study, they subjected the birds to three different temperature conditions: Warm, normal (control) and slowly increasing. They found that only the third condition had a significant effect on yawning frequency. Their conclusion is that yawning functions as a brain-cooling mechanism, much like a cooling fan on a laptop. When the environment is cooler than the body/brain temperature, taking air in quickly will function to cool the facial blood, which in turn will cool the brain. This leads to an increase in arousal, so those early morning yawns may function similar to a cup of coffee in providing a jolt of energy.
This explains the most common occurrences of yawning. Exhaustion and sleep-deprivation have been shown to increase brain temperature, so yawning in these states would make sense. In addition, yawning may be able to be used as signs of brain cooling problems, which occur in diseases such as multiple sclerosis.
The authors also point out that yawning should no longer be viewed as a sign of boredom, but as an indication of attentiveness. I will try to remember that during my next PowerPoint lecture.