We fitted the optical to mid-infrared (MIR) spectral energy distributions (SEDs) of ~15000 type-I, 0.75<z<2, active galactic nuclei (AGNs) in an attempt to constrain the properties of the physical component responsible for the rest-frame near-infrared (NIR) emission. We combine optical spectra from the Sloan Digital Sky Survey (SDSS) and MIR photometry from the preliminary data release of the Wide Infrared Survey Explorer (WISE). The sample spans a large range of AGN properties: luminosity, black hole mass, and accretion rate. Our model has two components: a UV-optical continuum source and very hot, pure-graphite dust clouds. We present the luminosity of the hot-dust component and its covering factor, for all sources, and compare it with the intrinsic AGN properties. We find that the hot-dust component is essential to explain the (rest) NIR emission in almost all AGNs in our sample, and that it is consistent with clouds containing pure-graphite grains and located between the dust-free broad line region (BLR) and the "standard" torus. The covering factor of this component has a relatively narrow distribution around a peak value of ~0.13, and it correlates with the AGN bolometric luminosity. We suggest that there is no significant correlation with either black hole mass or normalized accretion rate. The fraction of hot-dust-poor AGNs in our sample is ~15-20%, consistent with previous studies. We do not find a dependence of this fraction on redshift or source luminosity.