We measured low-temperature heat capacities of two-dimensional Fermi liquid (2D FL) formed on Hectorite down to 15mK. At a coverage where mean atomic distance is comparable to that of bulk3He liquid, we found that the temperature dependence deviates considerably from the expected linearity. To account for the deviation we carried through integrals including RPA spin susceptibility for the Stoner-Hubbard(SH) or the Landau's Fermi liquid (LFL) models over the effectively entire, energy-momentum space without imposing the paramagnon approximation or the like. We found numerically that the spin fluctuation develops a T2correction at T<T* which, at T>T*, is taken over by a Tlog T term where T* is some hundredths of TF. With these corrections we are able to interprete the data and have determined the parameters for each model consistently at the densities observed.