By using the microscopic sdgIBM-F-max 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 Pd-104
are carried out. The calculated values are coincident with the experimental
data reported recently. The results predict that the shape phase transitio
n in the groundstate band appears at about T approximate to 0.230 MeV and t
he phase transition of the thermal excitation mode takes place at T approxi
mate to 0.630 MeV for the nucleus Pd-104.