We present high-resolution $^{12}$CO and $^{13}$CO 2-1 ALMA observations, as well as optical and near-infrared spectroscopy, of the highly-inclined protoplanetary disk around SSTC2D J163131.2-242627. The spectral type we derive for the source is consistent with a $rm 1.2 , M_{odot}$ star inferred from the ALMA observations. Despite its massive circumstellar disk, we find little to no evidence for ongoing accretion on the star. The CO maps reveal a disk that is unusually compact along the vertical direction, consistent with its appearance in scattered light images. The gas disk extends about twice as far away as both the submillimeter continuum and the optical scattered light. CO is detected from two surface layers separated by a midplane region in which CO emission is suppressed, as expected from freeze-out in the cold midplane. We apply a modified version of the Topographically Reconstructed Distribution method presented by Dutrey et al. 2017 to derive the temperature structure of the disk. We find a temperature in the CO-emitting layers and the midplane of $sim$33 K and $sim$20 K at $rm R<200$ au, respectively. Outside of $rm R>200$ au, the disks midplane temperature increases to $sim$30 K, with a nearly vertically isothermal profile. The transition in CO temperature coincides with a dramatic reduction in the sub-micron and sub-millimeter emission from the disk. We interpret this as interstellar UV radiation providing an additional source of heating to the outer part of the disk.
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