With the help of numerical code, we simultaneously follow the time evolution of a large number of supernova remnants and superbubbles in a stratified medium, and from there infer the filling factor of hot cavities near the Sun. We find that superbubbles give a much larger contribution than individual supernova remnants, particularly at high Galactic altitudes. Our derived hot gas filling factor is approximately equal to 30% at the midplane and increases rapidly with height, reaching approximately 80%-90% at 2 kpc.
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K. Ferrière (1995) studied this question.