FD-SOI five-gate (5G) qubit MOS devices are electrically characterized in linear regime down to deep cryogenic temperatures. The Lambert-W function is successfully used for the modelling of such 5G MOS devices from subthreshold regime to strong inversion. Its applicability is demonstrated down to 20 K. The 5G device is modeled as a series of five independent transistors: the “active” one, that directly controls the current, and the “external” ones, that act as access resistances. The Lambert-W function enables to accurately determine the inversion charge and the active channel resistance from weak to strong inversion. This approach allows reconstructing the drain current characteristic avoiding the evaluation of the mobility attenuation factors. The main device parameters are extracted versus temperature. Finally, the role of different scattering mechanisms has been investigated, underlying the impact of neutral defects for the gates in proximity of source and drain.