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The warm absorbers observed in more than half of all nearby active galactic nuclei are tracers of ionized outflows located at parsec-scale distances from the central engine. If the smallest inferred ionization parameters correspond to plasma at a few 104 K, then the gas undergoes a transition from being bound to unbound, provided it is further heated to ∼106 K at larger radii. Dannen et al. recently discovered that, under these circumstances, thermally driven wind solutions are unsteady and even show very dense clumps due to thermal instability. To explore the observational consequences of these new wind solutions, we compute line profiles based on the one-dimensional simulations of Dannen et al. We show how the line profiles from even a simple steady-state wind solution depend on the ionization energy (IE) of absorbing ions, which is a reflection of the wind ionization stratification. To organize the diversity of the line shapes, we group them into four categories: weak Gaussians, saturated boxy profiles with and without an extended blue wing, and broad weak profiles. The lines with profiles in the last two categories are produced by ions with the highest IE that probe the fastest regions. Their maximum blueshifts agree with the highest flow velocities in thermally unstable models, both steady-state and clumpy versions. In contrast, the maximum blueshifts of the highest-IE lines in thermally stable models can be less than half of the actual solution velocities. Clumpy solutions can additionally imprint distinguishable absorption troughs at widely separated velocities. [ABSTRACT FROM AUTHOR]