  We calculate analytically the quantum and thermal fluctuations corrections of
a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these
fluctuations may change their character from repulsion to attraction in the
density-temperature plane owing to the striking momentum dependence of the
dipole-dipole interactions. The dipolar instability is halted by such
unconventional beyond mean field corrections leading to the formation of a
droplet phase. The equilibrium features and coherence properties exhibited by
such droplets are deeply discussed. At finite temperature, we find that the
equilibrium density crucially depends on the temperature and on the confinement
strength and thus, a stable droplet can exist only at ultralow temperature due
to the strong thermal fluctuations.
