  In this paper, the influence of an in-plane magnetic field B_\parallel on the
finite-temperature phase transitions in nu=2 bilayer quantum Hall systems are
examined. It is found that there can exist two types of finite-temperature
phase transitions. The first is the Kosterlitz-Thouless (KT) transitions, which
can have an unusual non-monotonic dependence on B_\parallel; the second type
originates from the crossing of energy levels and always increases with
B_\parallel. Based on these results, we point out that the threshold
temperature observed in the inelastic light scattering experiments cannot be
the KT transition temperature, because the latter shows a totally different
B_\parallel-dependence as compared with the experimental observation. Instead,
it should be the level-crossing temperature, which we found agrees with the
B_\parallel-dependence observed. Moreover, combining the knowledge of these two
transition temperatures, a complete finite-temperature phase diagram is
presented.
