Today, shape memory alloys (SMAs) have important applications in several fields of science and engineering. This work reports the thermomechanical behavior of NiTi SMA coil springs. The thermomechanical characterization is approached starting from mechanical loading–unloading tests under different electric current intensities, from 0 to 2.5 A. In addition, the material is studied using dynamic mechanical analysis (DMA), which is used to evaluate the complex elastic modulus E* = E′− iE″, obtaining a viscoelastic response under isochronal conditions. This work further evaluates the damping capacity of NiTi SMA using tan δ, showing a maximum around 70 °C. These results are interpreted under the framework of fractional calculus, using the Fractional Zener Model (FZM). The fractional orders, between 0 and 1, reflect the atomic mobility of the NiTi SMA in the martensite (low-temperature) and austenite (high-temperature) phases. The present work compares the results obtained from using the FZM with a proposed phenomenological model, which requires few parameters for the description of the temperature-dependent storage modulus E′.