Hi jc031662,
I don’t have any personal experience with the smell of a new Tempurpedic so I can’t make any comments about what they smell like to me but hopefully some of the other members here that own one will see your comments and share their experience.
The smell itself is most likely from some type of aldehyde which can range from very unpleasant, musty, or acrid with lower molecular weight aldehydes to the much more pleasant smells of higher molecular weight aldehydes that are in many essential oils or that are used in perfumes, cosmetics, soaps, and many other household products.
There are also some suggestions in post #3 here that may be helpful to help reduce any offensive smells and odors more quickly.
I should also mention that unlike many other manufacturers … Tempurpedic mattresses don’t have any certifications for VOC’s (see post #2 here).
Phoenix