We performed the heat capacity, C(T), measurement under high pressure for a ferromagnetic superconductor UGe2. At 1.15 GPa, we found a peak in C/T at a characteristic temperature, T-* = 6 K where the magnetization showed anomalous increase. At 1.28 GPa, above the critical pressure P-c(*) where T-* becomes 0 K, C/T does not show notable anomaly at zero magnetic field, but the application of the external field above 2.5 T induces the peak again at T-* > 0 K. It corresponds to the induction of T-* by the magnetic field. Our experimental result suggests that a second order phase transition takes place at T-* and thus a disappearance of the phase transition at T-* is of second order.