A model for computing the absorption spectrum of a diatomic adsorbed on a nonzero temperature surface is developed based on the exact time-dependent expression for the absorption spectrum averaged over the surface variables. The required time evolution of the dipole transition density operator is modeled by a quantum Langevin-type equation derived by the method of Caldeira and Leggett. The resultant equation is treated numerically and sample spectra are obtained for IBr on an MgO(001) surface at a temperature of 150 K. The results, parameterized by a diatom-surface coupling constant, characterize the broadening of the spectrum in the presence of the stochastic thermal substrate motion.