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For the first time, by taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of wavefunctions within d(3) electronic configuration, the values of parameters in expressions of Raman and optical-branch terms of thermal shifts (TS) due to EPI for three levels, T-4(2) band and T-4(1) band of ruby have been evaluated; the contributions to TS of T-4(2) and T-4(1) broad bands from thermal expansion have also been. calculated; and then, the TS of the peak energies of 'T2 and 4 Ti broad bands have been calculated. The results are in satisfactory agreement with observed data. The values of single-electron reduced matrix elements representing the strengths of EPI of T-4(2) and T-4(1) bands have respectively been determined. For TS of the peak energies of T-4(2) and T-4(1) bands, it is found that the contribution to TS from the second-order term in EPI Hamiltonian is dominant; TS due to EPI of acoustic branches are over two times as much as those of optical branches, and both of them increase rapidly with temperature; the neighbor-level term is insignificant; the contribution to TS from thermal expansion is specially important, and all the three terms of TS of T-4(2) or T-4(1) band axe red shifts.