The specific heat and susceptibility data for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ on Grafoil are analyzed in the framework of the Landau Fermi-liquid theory. The data suggest that the dominant interaction between ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ 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 ${\mathit{T}}_{\mathit{c}}$ is very small (∼${10}^{\mathrm{-}2}$–${10}^{\mathrm{-}3}$ depending on the form of the potential). For moderate areal densities of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${\mathit{T}}_{\mathit{c}}$ 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 ${\mathit{T}}_{\mathit{k}}$=3.2 mK is discussed.

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