Yes, Warmup has developed heaters that can be safely used under carpet and floating floors. Have a look at our Heating Carpet and Floating Floors page.
Foil mats use a similar cable technology, but embedded in multiple layer of laminated foil. The foil and the thin transfer grid work as heat dissipators under the carpet. This is necessary because neither the carpet or the pad are good heat conductors. Under tile and stone, the system relies on the mortar and the tile to carry the heat, but under carpet and laminates, the foil and carbon systems have to perform the job differently. This system is UL approved, has been on the market for over 2 decades and is a fantastic solution for cold bedrooms and basements.