This is a clip from research on the
pillow positive, in treatement of snoring and apnea, although they are stating improvement, I think you can see, it is very minimal and a very small sample group.
The researchers evaluated the RDI for 12 subjects with mild to severe sleep apnea, first while sleeping with their regular pillow and then with the specially shaped foam pillow. The average RDI for the three subjects with mild symptoms decreased from 14.7 to 10.5 after shifting to the new head support.
Patients with moderate to severe symptoms showed no significant improvement in their RDI.
A second study examined fifteen new subjects with mild sleep apnea and found a significant decrease in average RDI from 15.3 to 11.6. The airway caliber of eight of these patients was also measured; each subject showed significant improvement.
http://news-service.stanford.edu/news/1999/june9/apnea-69.html
I don't think any research exists for the tempurpedic pillow you asked about, but this is similar enough, I wanted to share this.