  We study the change in cosmic-ray pressure, the change in cosmic-ray density,
and the level of cosmic-ray induced heating via Alfven-wave damping when cosmic
rays move from a hot ionized plasma to a cool cloud embedded in that plasma.
The general analysis method outlined here can apply to diffuse clouds in either
the ionized interstellar medium or in galactic winds. We introduce a
general-purpose model of cosmic-ray diffusion building upon the hydrodynamic
approximation for cosmic rays (from McKenzie & Voelk and Breitschwerdt and
collaborators). Our improved method self-consistently derives the cosmic-ray
flux and diffusivity under the assumption that the streaming instability is the
dominant mechanism for setting the cosmic-ray flux and diffusion. We find that,
as expected, cosmic rays do not couple to gas within cool clouds (cosmic rays
exert no forces inside of cool clouds), that the cosmic-ray density does not
increase within clouds (it may slightly decrease in general, and decrease by an
order of magnitude in some cases), and that cosmic-ray heating (via Alfven-wave
damping and not collisional effects as for ~10 MeV cosmic rays) is only
important under the conditions of relatively strong (10 micro-Gauss) magnetic
fields or high cosmic-ray pressure (~10^{-11} ergs cm^{-3}).
