New heat capacity measurements of He-3 thin films adsorbed on Grafoil
have been made down to 0.3 mK for areal densities where the 2nd layer
solid He-3 shows 2D nuclear magnetism. The data show rounded maxima at
around 3 mK and 1/T-2 behavior at higher temperatures, while roughly
T-linear behavior below 2 mK. We did not observe any signs of finite t
emperature phase transitions nor additional structure in the heat capa
city, which is in sharp contrast to 3D solid He-3.