Nonisothermal kinetics of smectic phase formation in a chiral liquid crystalline (LC) azodye polymer is studied. The Ozawa exponent value of n similar to 2.5 is estimated for narrow polymer fractions with M-w/M-n similar to 1.3-1.6 but a temerature-dependent value, 0.5 < n < 1.2, for the raw polymer of M-w/M-n similar to 2.6. The effect of molar mass on mesomorphism is studied, and the dependence of melting temperature on subsequent heating from the rate of previous cooling, r, is theoretically explained. The narrow fractions show a "bistable" phase behavior forming conventional Sm A phase on slow cooling, r < 1 K/min, but another (probably a highly twisted TGB A*) mesophase on fast cooling, r > 1 K/min. A theoretical model for such a behavior is suggested, and the structure of the two phases is studied by SAXS. The applicability of the Kissinger approach to estimation of activation energy for TGB A* phase formation is discussed.