Does military tricare cover tempur-pedic bed?

Possibly. Tricare, the insurance provider for the American military, offers a variety of plans at a variety of prices, so a Temper-pedic bed might not be available in the plan the Marine-soldier-sailor-airman has chosen. However if a special bed such as a Temper-pedic is required for medical reasons, most likely it or a similar-but-cheaper unit will most likely be made available.