The specific heat and susceptibility data for He3 on Grafoil are analyzed in the framework of the Landau Fermi-liquid theory. The data suggest that the dominant interaction between He3 quasiparticles is an attraction in the p-wave channel. We have calculated explicitly the superfluid transition temperature in a two-dimensional Fermi gas and found that the prefactor in Tc is very small (∼10-2-10-3 depending on the form of the potential). For moderate areal densities of He3, Tc is estimated to be on the scale of several millikelvin. The relevance of these results to the change in the temperature behavior of the specific heat observed below Tk=3.2 mK is discussed.