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The effect of phonon modes and electron-hole pair (elhp) couplings at different surface temperature on 2(v = 0, 1; j = 0)-(111) collision has been explored by assuming weakly correlated interactions between molecular Degrees of Freedoms (DOFs) with surface modes and elhp excitations through a Hartree product type wavefunction, where the initial state distributions for the phonon modes and the elhp couplings are incorporated by using Bose-Einstein and Fermi-Dirac probability factors, respectively. We carry out four (4D⊗2D)- and six (6D)- dimensional quantum dynamics on such an effective Hamiltonian, and depict the calculated sticking/transition probabilities and energy transfer from molecule to the surface. The phonon modes slightly affect the sticking probability by broadening the profile, but the transition probability are substantially changed with respect to the rigid surface. On the contrary, the inclusion of elhp coupling along with phonon modes does not change the results much compared to the only phonon case. We formulate an effective Hamiltonian for D2 ( v = 0, 1; j = 0)-Cu(111) collision processes from first principle to include the surface temperature through phonon modes and electron-hole pair couplings, where the barrier (ttb, bth) heights of the potential undergo change substantially both with respect to time and temperature, and become responsible for the broadening of sticking probability and modifying the transition probability. The figure shows as the collision energy increases, the transition probability attends a saturation as predicted by experimental observation. For the system D2 ( v = 0, 1; j = 0)-Cu(111), the major contribution due to surface temperature arises from phonon modes, where the electron-hole pair coupling has minor effect on calculated probabilities as obtained by other contemporary theoretical calculations. [ABSTRACT FROM AUTHOR]