Carpet and foam padding will slow down but won't prevent the transfer of heat to the living space. For a stretched-carpet installation, use tackless strips. Just be extra careful when securing them with concrete nails - you don't want to puncture a buried copper line. While radiant lines usually are kept 3 in. away from outside walls, some installers don't adhere to this rule. What's more, lines are often run from room to room beneath interior walls.
Infrared thermography can accurately pinpoint copper lines and detect any leaks.
The best time to hire a certified infrared thermographer is as part of your prepurchase home inspection.