  Models that reproduce the observed high-velocity clouds (HVCs) also predict
clouds at lower radial velocities that may easily be confused with Galactic
disk (|z| < 1 kpc) gas. We describe the first search for these low-velocity
halo clouds (LVHCs) using IRAS data and the initial data from the Galactic
Arecibo L-band Feed Array survey in HI (GALFA-HI). The technique is based upon
the expectation that such clouds should, like HVCs, have very limited infrared
thermal dust emission as compared to their HI column density. We describe our
'displacement-map' technique for robustly determining the dust-to-gas ratio of
clouds and the associated errors that takes into account the significant
scatter in the infrared flux from the Galactic disk gas. We find that there
exist lower-velocity clouds that have extremely low dust-to-gas ratios,
consistent with being in the Galactic halo - candidate LVHCs. We also confirm
the lack of dust in many HVCs with the notable exception of complex M, which we
consider to be the first detection of warm dust in HVCs. We do not confirm the
previously reported detection of dust in complex C. In addition, we find that
most Intermediate- and Low-Velocity clouds that are part of the Galactic disk
have a higher 60 micron/100 micron flux ratio than is typically seen in
Galactic HI, which is consistent with a previously proposed picture in which
fast-moving Galactic clouds have smaller, hotter dust grains.
