Under the condition of electron-LO-phonon strong coupling, the eigen-energy and corresponding eigen-wave functions of the ground state and first excited state of electron in quantum disk were obtained by solving the energy eigen-equation precisely. The phonon effect and temperature effect were studied by unitary transformation and elementary excitation theory method. Furthermore, the temperature effect on the ground energy of the polaron in quantum disk was also discussed. Numerical results showed that few phonons were excited at low temperature, while in the condition of high temperature, the energy of polaron was effected by temperature, and the higher temperature, the more phonons. The results also indicated that the energy of the ground state of polaron decreased with the increasing electron-LO phonon coupling strength. It means that quantum disk has obvious quantum size effect.