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.
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