  We present a study of the ionization and thermal structure of neutral
hydrogen clouds located in the Galactic halo, immersed in the extragalactic
background radiation field, and supposed to be in pressure equilibrium with the
surrounding (presumably) hot medium. The problem is solved numerically, but an
useful analytical approximation has been derived as well. We discuss the two
main parameters of the problem, \ie the radiation field and the halo pressure,
in the framework of the current models for the halo/disk interaction. We find a
well defined relation between a critical column density at which the cloud
starts to develop a cold central core with the cloud linear size. Making use of
this relation, we suggest a straightforward method to derive the distance to
the cloud. We discuss the possible sources of error in this determination and
it is found that the method is particularly suitable for those clouds which are
subsonic with respect to the surrounding medium, while for the supersonic ones,
the method can only give a lower limit to the distance. The H$\alpha$ emission
from the partially ionized edge of the cloud is calculated and compared with
the available observations; this measure is a powerful indicator of the
possible presence of a shock in the cloud.
