We report a sizable class of type 1 active galactic nuclei (AGNs) with unusually weak near-infrared (1-3 Delta *mm) emission in the XMM-COSMOS type 1 AGN sample. The fraction of these 'hot-dust-poor' AGNs increases with redshift from 6% at low redshift (z < 2) to 20% at moderate high redshift (2 < z < 3.5). There is no clear trend of the fraction with other parameters: bolometric luminosity, Eddington ratio, black hole mass, and X-ray luminosity. The 3 Delta *mm emission relative to the 1 Delta *mm emission is a factor of 2-4 smaller than the typical Elvis et al. AGN spectral energy distribution (SED), which indicates a 'torus' covering factor of 2%-29%, a factor of 3-40 smaller than required by unified models. The weak hot dust emission seems to expose an extension of the accretion disk continuum in some of the source SEDs. We estimate the outer edge of their accretion disks to lie at (0.3-2.0) X 104 Schwarzschild radii, ~10-23 times the gravitational stability radii. Formation scenarios for these sources are discussed.