What a Uniform Heating Term Can and Cannot Do to Thermal Instability

Thermal instability — the runaway cooling of slightly overdense gas in pressure balance with its surroundings — organises the phase structure of the interstellar and circumgalactic media. This paper asks what happens to it when the net cooling rate acquires a density-independent heating term Q = f u_L / t_H fed by the surviving vacuum density, with u_L = 5.25e-09 erg per cubic centimetre. The answer divides cleanly. Field's instability criteria, both isochoric and isobaric, are exactly unchanged: a constant Q drops out of the temperature derivatives that define them, a fact verified analytically and numerically here (the isochoric-unstable band of the adopted cooling curve remains 1.12e5 to 1.12e7 K for any f). What Q changes is everything around the criteria: equilibria against the heating floor alone exist only above a critical density n_crit = sqrt(Q / Lambda_max), which is 1.28e-06 per cubic centimetre at f = 1e-08; and the instability's growth time is stretched by the factor S = 1 / (1 - Q / (n^2 Lambda)), which reaches 10 in circumgalactic gas at f = 1.57e-03, in hot interstellar gas at f = 1.00e-02, and would require the unphysical value f = 10.3 in the warm neutral medium. A uniform heating term cannot redraw the stability map, but near the balance point it freezes the instability in place. Computed from stated assumptions; not a measurement.