A bead core for locking a tire to a seat of a wheel rim includes a plurality of annular reinforcement elements having an inner transverse dimension smaller than a maximum diameter of the wheel rim, and being sufficiently deformable at ambient temperature to facilitate mounting the tire onto the wheel rim. The plurality of annular reinforcement elements includes at least one tightening element made of a shape-memory alloy responsive to temperature increases by increasing a tightening force on the wheel rim at a predetermined temperature. A tire including the bead core and a method for securing a tire to a rim using the bead core are also disclosed.