X-ray emitting diffuse nebulae around hot stars are observed to have soft-band temperatures in the narrow range 1 to 3 million degrees Kelvin, independent of the characteristics 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) and Wolf-Rayet nebulae (WR) around evolved stars 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 numerical simulations and combine these with the X-ray emission coefficient for the 0.3--2.0 keV band to estimate the X-ray temperature of the hot gas.We find that all the simulated diffuse 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 photoionized gas. Sharply peaked emission coefficients act as efficient 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. We suggest that turbulent mixing layers are the origin of the soft X-ray emission in all these diffuse nebulae.