We have measured the heat capacity of He-3 thin films adsorbed on grap
hite at an areal density of 15.0 nm(-2) down to as low as 100 mu K. Th
e second-layer He-3 behaves as a degenerate 2D Fermi fluid in the whol
e temperature range we studied. We observed no anomalous behavior in t
he heat capacity near 3 mK in contradiction to the recent report by ot
her workers. This indicates that possible superfluid transitions would
be below 100 mu K. Instead, a small and temperature-independent contr
ibution to the heat capacity teas observed, which we attribute to nucl
ear-spin degrees of freedom in glassy solid He-3 trapped in substrate
heterogeneities.