  The specific heat of a two-layer He-4 film adsorbed on a graphite substrate
is estimated as a function of temperature by Quantum Monte Carlo simulations.
The results are consistent with recent experimental observations, in that they
broadly reproduce their most important features. However, neither the
"supersolid" nor the "superfluid hexatic" phases, of which experimental data
are claimed to be evidence, are observed. It is contended that heat capacity
measurements alone may not be a good predictor of structural and superfluid
transitions in this system, as their interpretation is often ambiguous.
