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By using the microscopic sdgIBM-Fmax approach, the procedure of canonical ensemble average and the saddle point approximation, the thermodynamics of the nucleus is established under microscopic IBM. Calculations of spectrum, level density and finite-temperature specific heat for the nucleus 104pd are carried out. The calculated values are coincident with the experimental data reported recently. The results predict that the shape phase transition in the groundstate band appears at about T ≈0.230MeV and the phase transition of the thermal excitation mode takes place at T ≈0.630 MeV for the nucleus 104pd.