Monte Carlo calculations of the specific heat of a model glass have been carried out to determine the thermodynamic consequences of the configurational constraints required to define a single glass state. Three different configurational constraints were employed. Using a cell model, we find a steady decrease in the heat capacity C-V with increasing temperature indicating a significant anharmonic behavior in the soft disk glass. If, instead, we constrain the particle fluctuations to uncoupled instantaneous normal modes (INM's), we find that the heat capacity is almost independent of temperature and equal to the harmonic value, even when the full anharmonic potential is used. To resolve this contradiction, we employ a tether constraint and find reasonable agreement with the cell model results. We conclude (i) that the harmonic behavior under the INM constraint is an artifact arising from the arbitrary restrictions on particle motions, and (ii) that the soft disk glass is an anharmonic solid with a heat capacity that decreases on heating along an isobar.