With straightforward modeling of the late evolution of supernova remnants, including a modest nonthermal contribution to the pressure in the preshock (ambient) gas, we demonstrate that in the solar neighborhood: 1.the porosity induced by the remnant population in a warm intercloud medium (n ∼0.15 cm-3) would not be large (q ≲ 0.2), and 2.the slowly cooling supernova remnant bubbles harbor large populations of the high-stage ions (O VI, N V, and C IV at least), sufficient to explain their mean densities in the galactic plane (though a comparable contribution may derive from OB association bubbles). With these results it is no longer clear that there is any need for a pervasive phase of hot gas in the interstellar medium, beyond that found within localized disturbances.
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Slavin et al. (1993) studied this question.