We investigate the influence of molecular vibrations on the tunneling of electrons through an octane-thiolate sandwiched between two gold contacts. The coherent and incoherent tunneling currents are computed using the non-equilibrium Green's functions formalism. Both the system Hamiltonian and the electron-phonon interaction are obtained from first-principles DFT calculations, including a microscopic treatment of the gold contacts. This method allows to study explicitly the influence of each individual vibrational mode and show a detailed analysis of the power dissipated in the molecular wire.