Using NASA IRTF SpeX data from 0.8 to 4.5 $mu$m, we determine self-consistently the stellar properties and excess emission above the photosphere for a sample of classical T Tauri stars (CTTS) in the Taurus molecular cloud with varying degrees of accretion. This process uses a combination of techniques from the recent literature as well as observations of weak-line T Tauri stars (WTTS) to account for the differences in surface gravity and chromospheric activity between the TTS and dwarfs, which are typically used as photospheric templates for CTTS. Our improved veiling and extinction estimates for our targets allow us to extract flux-calibrated spectra of the excess in the near-infrared. We find that we are able to produce an acceptable parametric fit to the near-infrared excesses using a combination of up to three blackbodies. In half of our sample, two blackbodies at temperatures of 8000 K and 1600 K suffice. These temperatures and the corresponding solid angles are consistent with emission from the accretion shock on the stellar surface and the inner dust sublimation rim of the disk, respectively. In contrast, the other half requires three blackbodies at 8000, 1800, and 800 K, to describe the excess. We interpret the combined two cooler blackbodies as the dust sublimation wall with either a contribution from the disk surface beyond the wall or curvature of the wall itself, neither of which should have single-temperature blackbody emission. In these fits, we find no evidence of a contribution from optically thick gas inside the inner dust rim.
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