We present new calculations on the contribution from cooling hot gas to the
photoionization of warm ionized gas in the Galaxy. We show that hot gas in
cooling supernova remnants (SNRs) is an important source of photoionizatio
n, particularly for gas in the halo. We find that in many regions at high l
atitude this source is adequate to account for the observed ionization, so
there is no need to find ways to transport stellar photons from the disk. T
he flux from cooling SNRs sets a floor on the ionization along any line of
sight. Our model flux is also shown to be consistent with the diffuse soft
X-ray background and with soft X-ray observations of external galaxies. We
consider the ionization of the clouds observed toward the halo star HD 9352
1, for which there are no O stars close to the line of sight. Along this li
ne of sight, two groups of clouds (densities similar to 0.3-1 cm(-3) and te
mperatures similar to 7000 K) are observed at similar to 0 km s(-1) ("slow"
) and similar to-50 km s(-1) ("fast"). We show that the observed ionization
can be explained successfully by our model EUV/soft X-ray Bur from cooling
hot gas. In particular, we can match the H alpha intensity, the S++/S+ rat
io, and the C+* column. Our models show that it is possible to account for
the observed ionization without invoking exotic ionization mechanisms such
as decaying neutrinos (Sciama). Our value for X-ray opacity along this line
of sight is somewhat larger than the average for the halo found by Arabadj
is & Bregman, but we do not regard the difference as significant. From obse
rvations of the ratios of columns of C+* and either S+ or H-0, we are able
to estimate the thermal pressure in the clouds. The slow clouds require hig
h (similar to 10(4) cm(-3) K) thermal pressures to match the NC+*/NS+ ratio
. Additional heating sources are required for the slow clouds to maintain t
heir similar to 7000 K temperatures at these pressures, as found by Reynold
s, Haffner, & Tufte. We also estimate the fraction of the line of sight tha
t is occupied by warm ionized and neutral gas and find it to be small, only
6%-9%.