ionized clouds at temperatures of 10$^4$ K in a Milky Way-sized galaxy, for which the RHG is heated to the virial temperature of $\approx$10$^6$ K. The smaller value of $D_{\rho}$ for Model 4 would be appropriate for either cooler backgrounds or warmer clouds.

The physical dimensions of the WFC’s are set by dynamical and thermal processes [@LM00]. Clouds below a minimum radius, $S_{min}$, are re-heated by conduction from the RHG. The maximum radius, $S_{max}$, is set by the point at which the clouds become self-gravitating. Such clouds have negative specific heats, and so are unstable to external heating. The lower limit upon the cloud size translates to [@LM00] $$S_{min,s}=1.6{\ T}^{3/2}_6{\ D}_{100}^{-1}{\ n}_{10}^{-1}
{\ }\Lambda_{25}^{-1}{\ \rm pc},$$ in the limit of saturated conduction, where $T_6$ in the temperature of the RHG in units of 10$^6$ K, $D_{100}$ is the density contrast between the cloud and RHG in units of 100, n$_{10}$ is number density of the cloud in units of 10 cm$^{-3}$, and $\Lambda_{25}$ is the cooling efficiency in units of 10$^{-25}$ ergs cm$^3$ s$^{-1}$, characteristic of low metallicity gas near 10$^4$ K [@DM72]. In the limit of unsaturated conduction, $$S_{min,u}=4{\rm T}^{7/4}_6{ \rm n}_{10}^{-1}
{\ }\Lambda_{25}^{-1/2}{\ \rm pc}.$$ The maximum cloud 