  We present a new method for using measured X-ray emission line fluxes from O
stars to determine the shock-heating rate due to instabilities in their
radiation-driven winds. The high densities of these winds means that their
embedded shocks quickly cool by local radiative emission, while cooling by
expansion should be negligible. Ignoring for simplicity any non-radiative
mixing or conductive cooling, the method presented here exploits the idea that
the cooling post-shock plasma systematically passes through the temperature
characteristic of distinct emission lines in the X-ray spectrum. In this way,
the observed flux distribution among these X-ray lines can be used to construct
the cumulative probability distribution of shock strengths that a typical wind
parcel encounters as it advects through the wind. We apply this new method
(Gayley 2014) to Chandra grating spectra from five O stars with X-ray emission
indicative of embedded wind shocks in effectively single massive stars.
Correcting for wind absorption of the X-ray line emission is a crucial
component of our analysis, and we use wind optical depth values derived from
X-ray line-profile fitting (Cohen et al. 2014) in order to make that
correction. The shock-heating rate results we derive for all the stars are
quite similar: the average wind mass element passes through roughly one shock
that heats it to at least $10^6$ K as it advects through the wind, and the
cumulative distribution of shock strengths is a strongly decreasing function of
temperature, consistent with a negative power-law of index $n \approx 3$,
implying a marginal distribution of shock strengths that scales as $T^{-4}$,
and with hints of an even steeper decline or cut-off above $10^7$ K.
