  We investigate the thermodynamic stability of quantized vortices in a dilute
Bose gas confined by a rotating harmonic trap at finite temperature.
Interatomic forces play a crucial role in characterizing the resulting phase
diagram, especially in the large $N$ Thomas-Fermi regime. We show that the
critical temperature for the creation of stable vortices exhibits a maximum as
a function of the frequency of the rotating trap and that the corresponding
transition is associated with a discontinuity in the number of atoms in the
condensate. Possible strategies for approaching the vortical region are
discussed.
