In this work, some physical properties of a commercial Ni–Ti (nitinol) shape-memory alloy with cylindrical geometry (wire) were investigated; the focus was on the thermomechanical, calorimetric and magnetic characterization. By dynamical mechanical analysis, the range of elasticity, the elasticity–viscoelasticity coexistence domain and the domain in which a maximum force is applied were determined for the SMA wire. By using the temperature-modulated differential scanning calorimetry method, a multi-step temperature variation program was applied to the wire with cylindrical geometry, in two stages (heating–cooling) and through the interpretation of heat fluxes (reversible, nonreversible and total), and the phase transitions in the formation of martensite, austenite and rhombohedral phase (R-phase) were identified and correlated with those observed during the thermomechanical study; also, the formation of austenite and martensite was evidenced by the regular differential scanning calorimetry method; by magnetic measurements, it was established that the SMA wire had magnetic properties at room temperature, and the nitinol sample is paramagnetic and linear in the intensity of the magnetizing magnetic field; these results were compared with those previously obtained for the investigation of the nitinol SMA stripe.