Is thermal instability significant in turbulent galactic gas?

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.