  Among the models proposed to account for the new component of diffuse EUV and
soft X-ray emission from clusters of galaxies (first discovered in Virgo) are
two key contestants: the non-thermal scenario which postulates a population of
relativistic electrons undergoing inverse-Compton (IC) interaction with the
cosmic microwave background, and the original conjecture that the radiation is
from a thermal warm gas at a temperature of $\sim$ 10$^{5-6}$ K. Currently a
consensus set of limiting values on cosmological parameters favor the thermal
gas interpretation. We also argued, based on pressure balance within the
intracluster medium (ICM), that the non-thermal approach has formidable
difficulties. Here we describe a spatial analysis of the soft X-ray excess
emission of three clusters (Virgo, A2199, and Coma), using archival ROSAT/PSPC
data, which reveals resolved features of cold intracluster clouds in absorption
spreading over vast distances. Within the sample there is good indication that
the soft excess radial trend (SERT, which qualitatively means a rising
importance of the soft component with cluster radius) is due to a centrally
peaked distribution of cold matter, with Coma having the least effect and no
direct evidence for absorption. The data strongly suggest an intermixed ICM
which contains gas masses at a wide range of temperatures, and the soft excess
is due to a warm intermediate phase.
