  We theoretically analyze the collective dynamics of a thermal beam of atomic
dipoles that couple to a single mode when traversing an optical cavity. For
this setup we derive a semiclassical model and determine the onset of
superradiant emission and its stability. We derive analytical expressions for
the linewidth of the emitted light and compare them with numerical simulations.
In addition, we find and predict two different superradiant phases; a
steady-state superradiant phase and a multi-component superradiant phase. In
the latter case we observe sidebands in the frequency spectrum that can be
calculated using a stability analysis of the amplitude mode of the collective
dipole. We show that both superradiant phases are robust against free-space
spontaneous emission and $T_2$ dephasing processes.
