Bed bugs can't live in a real Tempurpedic mattress, it's one of their many benefits.
EDIT: never mind, I guess I was sold a false bill of goods. Apparently, there have been reports done that prove dust mites can live in Tempurpedic mattresses because dust mites live on us.
The only way to prevent allergy-provoking dust mites in your mattress is to use dust-mite resistant encasings and covers but even they aren't 100% effective. This is why "dust-mite free" claims are a fallacy. No memory foam mattress is free of mites. It is true, however, that its extremely dense structure makes it more difficult for dust mites to nest and feed.
Foam, however, be it the visco elastic kind or not, be it from Tempurpedic or not, does not promote dust mite growth because, unlike natural fibres, is not a food source in itself. This is what mite-resistant means.
Tempur memory foam beds don't stop mites feeding on your dead skin cells, it just means that they are not a feeding source in themselves. They are, therefore, indeed made of a naturally resistant material to dust mites but so are all foam beds, even latex beds.
The Tempur-Pedic website makes the following statement:
Tempurpedic beds are naturally treated to be resistant to mites and other household allergens. Our products are also CFC (chlorofluorocarbon) and formaldehyde free
While a Tempur-Pedic bed is indeed allergy and dust-mite resistant, the fact is that any foam mattress is also dust-mite and allergy-resistant. Again, this does not mean they are mite-free or that they stop these bugs from feeding on dead skin cells.