  We investigate the impact of the far ultraviolet (FUV) heating rate on the
stability of the three-phase interstellar medium using three-dimensional
simulations of a $1$ kpc$^2$, vertically-extended domain. The FUV heating rate
sets the range of thermal pressures across which the cold ($\sim10^2$ K) and
warm ($\sim10^4$ K) neutral media (CNM and WNM) can coexist in equilibrium.
Even absent a variable star formation rate regulating the FUV heating rate, the
gas physics keeps the pressure in the two-phase regime: because radiative
heating and cooling processes happen on shorter timescales than sound wave
propagation, turbulent compressions tend to keep the interstellar medium within
the CNM-WNM pressure regime over a wide range of heating rates. The thermal
pressure is set primarily by the heating rate with little influence from the
hydrostatics. The vertical velocity dispersion adjusts as needed to provide
hydrostatic support given the thermal pressure: when the turbulent pressure
$\langle\rho\rangle\sigma_z^2$ is calculated over scales $\gtrsim500$ pc, the
thermal plus turbulent pressure approximately equals the weight of the gas. The
warm gas volume filling fraction is $0.2<f_w<0.8$ over a factor of less than
three in heating rate, with $f_w$ near unity at higher heating rates and near
zero at lower heating rates. We suggest that cosmological simulations that do
not resolve the CNM should maintain an interstellar thermal pressure within the
two-phase regime.
