Thermal instability in turbulent models of the Interstellar Medium

We discuss numerical simulations (and issues) of the atomic ISM tailored to investigate the possible existence of significant amounts of gas in the temperature range between the warm and cold stable phases. We attribute the presence of this gas to two facts: the enhanced stability of moderate, adiabatic-like velocityfluctuations occurring when the ratio of the cooling to the dynamical crossingtime is large, and the recycling of gas from the denseto the diffuse phase by stellar energy injection. Weconclude by suggesting that the gas with unstable temperatures can beobservationally distinguished through simultaneous determination of twoof its thermodynamic variables.