(Abridged) We discuss the nonlinear development of the isobaric mode of thermal instability (TI) in the context of the atomic interstellar medium (ISM), in order to assess the ability of TI to establish a well-segregated multi-phase structure in the turbulent ISM. The key parameter is the ratio of the cooling time to the dynamical crossing time η. The isobaric density perturbations of sizes ≳ 15 pc in media with mean density ∼ 1 cm^-3 develop inflow motions with Mach number larger than 0.5 and

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... shock that propagates outwards from the condensation and brings the surrounding medium out of thermal equilibrium. The time for the dynamical transient state to subside ranges from 4 to 30 Myr for initial density perturbations of 20 sizes 3 to 75 pc. By the time the condensations have formed, a substantial fraction of the mass is still traversing the unstable range and, therefore, clouds formed by TI should be bounded by accreting gas traversing the unstable range, rather than by sharp transitions to the stable warm phase. In the presence of random velocity forcing the condensation process can be suppressed for arbitrarily long times if the forcing causes a moderate rms Mach number (≳ 0.3) and extends to small enough scales that η>1. We suggest that these mechanisms may be at the origin of the relatively large amounts of gas mass in the unstable regime. We remark that in the (stable) warm diffuse medium, η>1 for velocity perturbations of scales up to several pc. The flow's response to them is thus nearly adiabatic, and relatively weakly compressible, consistent with observations that suggest a nearly Kolmogorov power spectrum in this medium.