Isobaric thermal stability of a two-level coolant

At fixed pressure and fixed composition, density varies as $T^{-1}$. With temperature-independent heating per particle, low-density cooling per particle scales as $T^{-3/2}{e}^{-\theta /T}$ and is restoring for $T<2\theta /3$. For constant heating per volume instead, the cooling scales as $T^{-5/2}{e}^{-\theta /T}$ and the threshold is $2\theta /5$. The heating normalization and perturbation constraint must be specified.