Using a highly sensitive torsional vibration technique, the authors have determined the critical temperatures of the superconducting transition (Tc) of individual phases of multiphase cuprates [Bi1.7Pb0.3Sr2Ca(n-1)CunOy (n = 2–30)] in a constant external magnetic field (H) in the temperature range of 77 to 270 K. It has been found that oscillation damping peaks are more pronounced when a sample is rapidly cooled in an external magnetic field (FC) to a temperature of 77 K and then is slowly warmed to room temperature. An increase in the time of sample exposure to a magnetic field at 77 K leads to a rise in the temperature Tc of different phases, and to an increase in the intensity of a signal corresponding to high-temperature phases with Tc > 240 K. Structural studies have shown that with increasing sample exposure time at 77 K, as a result of sample compression an increase in stress concentration at grain boundaries appears to increase defect density and to enhance the pinning of Abrikosov vortices, i.e. creates new (additional) conditions for their “freezing” during the field cooling (FC) procedure. It has been established that in samples of the Bi1.7Pb0.3Sr2Ca(n-1)CunOy (n = 2–30) series, the critical temperature Tc increases from 107 K to ≥ 240 K with an increase in n.