The long-time behavior of thermally unstable one-dimensional disturbances in an optically thin ionized gas, subject to external heating and radiative cooling, is investigated. The intermediate-wavelength limit is considered, corresponding to the most rapidly growing isobaric condensation mode. The "reaction-diffusion" equation, describing the instability dynamics in Lagrangian coordinates, is employed to study the time evolution of small sinusoidal initial perturbations away from the unstable thermal equilibrium. On the relatively short heating-cooling time scale, steep temperature and density fronts develop in the gas, corresponding to spatial coexistence of two locally stable thermal equilibria adjacent to the unstable one on the isobaric heating-cooling curve. It is shown, however, that only one of these states generally survives on the much longer heat conduction time scale. The numerically observed transition to the final "truly" stable state is interpreted in terms of the interaction between traveling temperature fronts which preserve their identity until annihilation.