This work is a study of the thermal stability of (001)-cut Pb (Mg1/3 Nb2/3) 1-x Tix O3 (x=0.30) single crystals before and after an electric (E) -field poling by means of dielectric permittivity, hysteresis loop, domain structure, polarization current, and x-ray diffraction. An R (RNT) -R (RNT) /T (TNT) -T (TNT) -C transition sequence was observed upon heating in the unpoled sample. R, RNT, T, TNT, and C are the rhombohedral, rhombohedral nanotwin, tetragonal, tetragonal nanotwin, and cubic phases, respectively. R/T indicates coexistence of the R and T phases. R (RNT) and T (TNT) indicate that the RNT and TNT structures mimic monoclinic phases in the R and T matrices, respectively. After a prior E -field poling, an R (RNT) -T (TNT) -C phase sequence takes place upon heating. The dielectric permittivity and current density evidenced an additional polarization at 355 K, which is associated with the vanishing of the dielectric dispersion, which reappears near 410 K and remains up to the Burns temperature TB =510 K. This study suggests that nanotwins (RNT and TNT) can play an important role in high-strain piezoelectric crystals while phase transition takes place. Under E=38 kV/cm,  T domains randomly appeared in the matrix, suggesting that the matrix consists of a glassy matrix and ferroelectric nanoclusters.