We present a novel technique for investigating the melting and crystallization of nanomaterials in confinement. According to this method, the melting-crystallization phase transitions are traced by sharp changes of viscoelastic properties of matter using quartz resonator Q-factor analysis during heating-cooling cycles. Ge/Bi/Ge layered films, formed by successive condensation of components in high vacuum, were used as the model of nanoscale Bi confined in Ge matrix. Size dependences of the melting and crystallization temperatures have been systematically determined for the samples with Bi film thickness of 5-50 nm. The obtained data are in good agreement with the data obtained previously using in situ transmission electron microscopy techniques.