Electron correlations in charge transfer complexes consisting of organic donor/acceptor molecules with their counter ions play an important role for realizing various kinds of ground states. Among numerous compounds, those classified as the dimer-Mott system such as κ-type and β’-type 2:1 complexes give a conducting/superconducting phase and a Mott insulating phase due to the difference of U/W ratio. In the conducting region, unconventional superconductors with Tc ≈ 10 K class appear at low temperatures. In order to cultivate new features and to verify the mechanism of them, we constructed several calorimetry systems for measuring heat capacity by small amount of samples with varying temperatures, magnetic fields and external pressures. The systematic heat capacity measurements of the superconductive phase revealed that the pairing symmetry is anisotropic d-wave accompanied by line-node gap structures. The angle resolved heat capacity measurements with in-plane magnetic fields detected a clear four-fold modulation of the electronic heat capacity coefficient. The importance of the antiferromagnetic spin fluctuations for pair formation is strongly suggested. In the dimer-Mott triangle lattice compounds, a spin liquid-like feature was observed from the analyses of low temperature heat capacity data under magnetic fields. The advantages of the heat capacity measurements to clarify the phase relations and to detect low energy excitations from the ground states are emphasized.