The impact of variation in the relative fractions of the ferromagnetic metallic and antiferromagnetic/charge ordered insulator phases on the supercooling/superheating transition in strongly phase separated system, La5/8−yPryCa3/8MnO3 (y ≈ 0.4), has been studied employing magnetotransport measurements. Our study clearly shows that the supercooling transition temperature is non-unique and strongly depends on the magneto-thermodynamic path through which the low temperature state is accessed. In contrast, the superheating transition temperature remains constant. The thermo-magnetic hysteresis, the separation of the two transitions and the associated resistivity, all are functions of the relative fraction of the coexisting phases.