The homogeneous vibrational line shape of an adatom on a surface is determined by its interactions with other localized and delocalized modes of the adsorbate and substrate. These interactions include anharmonic bonds between the adatom and the surface, and also between the substrate atoms themselves at the adsorption site. The line width and frequency shift of the perpendicular vibrational mode of an adatom at a bridge site is calculated as a function of temperature, due to coupling to phonon modes of a semi-infinite elastic continuum. A self energy formulation is employed, using perturbative methods in a quantum field theory. The effects of anharmonicity of both the adsorption bonds and of the interatomic bonds between substrate atoms at the bridge site, on the vibrational line shape, are compared. Energy relaxation by two-phonon emission is found to describe well the temperature-dependent line width in the O Cu(110) system.