The quantum transduction of an rf/microwave signal to the optical domain, and vice versa, paves the way for technologies that exploit the advantages of each domain to perform quantum operations. Since electro-optomechanical devices implement a simultaneous coupling of a mechanical oscillator to both an rf/microwave field and an optical field, they are suitable for the realization of a quantum transducer. The membrane-in-the-middle setup is a possible solution, once its vibrational mode is cooled down to ultra cryogenic temperature for achieving quantum operation. This work is focused on the mechanical characterization via an optical interferometric probe, down to T = 18 mK , of a loss-shielded metalized membrane designed for this purpose. A stroboscopic technique has been exploited for revealing a mechanical quality factor up to 64 × 10 6 at the lowest temperature. In fact, with continuous illumination and a cryostat temperature below 1 K , the heat due to optical absorption is not efficiently dissipated anymore, and the membrane remains hotter than its environment.