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.

PACS numbers: 74.25.Bt, 74.70.Tx, 74.62.Fj