On the X-ray temperature of hot gas in diffuse nebulae
  X-ray emitting diffuse nebulae around hot stars are observed to have
soft-band temperatures in the narrow range [1-3]$\times10^{6}$ K, independent
of the stellar wind parameters and the evolutionary stage of the central star.
We discuss the origin of this X-ray temperature for planetary nebulae (PNe),
Wolf-Rayet nebulae (WR) and interstellar wind bubbles around hot young stars in
our Galaxy and the Magellanic Clouds. We calculate the differential emission
measure (DEM) distributions as a function of temperature from previously
published simulations and combine these with the X-ray emission coefficient for
the 0.3-2.0 keV band to estimate the X-ray temperatures. We find that all
simulated nebulae have DEM distributions with steep negative slopes, which is
due to turbulent mixing at the interface between the hot shocked stellar wind
and the warm photoionised gas. Sharply peaked emission coefficients act as
temperature filters and emphasize the contribution of gas with temperatures
close to the peak position, which coincides with the observed X-ray
temperatures for the chemical abundance sets we consider. Higher metallicity
nebulae have lower temperature and higher luminosity X-ray emission. We show
that the second temperature component found from spectral fitting to X-ray
observations of WR nebulae is due to a significant contribution from the hot
shocked stellar wind, while the lower temperature principal component is
dominated by nebular gas. We suggest that turbulent mixing layers are the
origin of the soft X-ray emission in the majority of diffuse nebulae.
