  We fit a new line shape model to \textit{Chandra} X-ray spectra of the O
supergiant $\zeta$ Puppis to test the robustness of mass-loss rates derived
from X-ray wind line profiles against different assumed heating models. Our
goal is to track the hot gas by replacing the common assumption that it is
proportional to the cool gas emission measure. Instead of assuming a turn-on
radius for the hot gas (as appropriate for the line-deshadowing instability
internal to the wind), we parametrize the hot gas in terms of a mean-free path
for accelerated low-density gas to encounter slower high-density material. This
alternative model is equally successful as previous approaches at fitting X-ray
spectral lines in the 5 -- 17 \AA\ wavelength range. We find that the
characteristic radii where the hottest gas appears is inversely proportional to
line formation temperature, suggesting that stronger shocks appear generally
closer to the surface. This picture is more consistent with pockets of
low-density, rapid acceleration at the lower boundary than with an internally
generated wind instability. We also infer an overall wind mass-loss rate from
the profile shapes with a technique used previously in the literature. In doing
so, we find evidence that the mass-loss rate derived from X-ray wind line
profiles is not robust with respect to changes in the specific heating picture
used.
