We investigate numerically the role of thermal instability (TI) as a genera
tor of density structures in the interstellar medium (ISM), both by itself
and in the context of a globally turbulent medium. We consider three sets o
f numerical simulations: (1) flows in the presence of the instability only;
(2) flows in the presence of the instability and various types of turbulen
t energy injection (forcing), and (3) models of the ISM including the magne
tic field, the Coriolis force, self-gravity and stellar energy injection. S
imulations in the first group show that the condensation process that forms
a dense phase ("clouds") is highly dynamical and that the boundaries of th
e clouds are accretion shocks, rather than static density discontinuities.
The density histograms (probability density functions [PDFs]) of these runs
exhibit either bimodal shapes or a single peak at low densities plus a slo
pe change at high densities. Final static situations may be established, bu
t the equilibrium is very fragile: small density fluctuations in the warm p
hase require large variations in that of the cold phase, probably inducing
shocks in the clouds. Combined with the likely disruption of the clouds by
Kelvin-Helmholtz instability, this result suggests that such configurations
are highly unlikely. Simulations in the second group show that large-scale
turbulent forcing is incapable of erasing the signature of TI in the densi
ty PDFs, but small-scale, stellar-like forcing causes the PDFs to transit f
rom bimodal to a single-slope power law, erasing the signature of the insta
bility. However, these simulations do not reach stationary regimes, with TI
driving an ever-increasing star formation rate. Simulations in the third g
roup show no significant difference between the PDFs of stable and unstable
cases and reach stationary regimes, suggesting that the combination of the
stellar forcing and the extra effective pressure provided by the magnetic
field and the Coriolis force overwhelm TI as a density-structure generator
in the ISM, with TI becoming a second-order effect. We emphasize that a mul
timodal temperature PDF is not necessarily an indication of a multiphase me
dium, which must contain clearly distinct thermal equilibrium phases, and t
hat this "multiphase" terminology is often inappropriately used.