Hi suziQ,
There is a lot more information in post #2 here and the more detailed posts and information it links to about safe, natural, organic, “chemical free”, and “green” mattresses and mattress materials that can help sort through some of the marketing information and terminology that you will encounter in the industry and can help you differentiate between them and answer “how safe is safe enough for me” that can help each person decide on the types of materials they are most comfortable having in their mattress or on the certifications that may be important to them. These types of issues are complex and are generally specific to each person and their individual sensitivities, circumstances, criteria, beliefs, and lifestyle choices.
The only reliable way to assess the “safety” of a material in more general terms is based on any laboratory testing and certifications they have for harmful substances and VOC’s (see post #2 here for more information about some of the reliable “safety” certifications) and Tempurpedic is not CertiPUR certified and doesn’t have any specific certifications for VOC’s that I’m aware of so there is really no way to know for certain. Anecdotally they have the most complaints about their smell and sensitivities to their material (see here) but they are also the most widely sold memory foam mattress as well so some of the frequency of complaints would be the result of the sheer number of mattresses they sell.
There is also a class action lawsuit against Tempurpedic regarding VOC’s in their mattresses (see here and here).
Phoenix