  We investigate the thermodynamics of the RR charged two-dimensional type-0A
black hole background at finite temperature, and compare with known 0A matrix
model results. It has been claimed that there is a disagreement for the free
energy between the spacetime and the dual matrix model. Here we find that this
discrepancy is sensitive to how the cutoff is implemented on the spacetime
side. In particular, the disagreement is resolved once we put the cutoff at a
fixed distance away from the horizon, as opposed to a fixed position in space.
Furthermore, the mass and the entropy of the black hole itself add up to an
analytic contribution to the free energy, which is precisely reproduced by the
0A matrix model. We also use results from the 0A matrix model to predict the
next to leading order contribution to the entropy of the black hole. Finally,
we note that the black hole is characterized by a Hagedorn growth in its
density of states below the Hagedorn temperature. This, together with other
results, suggests there is a phase transition at this temperature.
