Accurately modeling surface temperature and surface motion e↵ects is necessary to study molecule-surface reactions in which the energy dissipation to surface phonons can largely a↵ect the observables of interest. We present here a critical comparison of two methods that allow to model such e↵ects, namely the ab initio molecular dynamics (AIMD) method and the generalized Langevin oscillator (GLO) model, using the dissociation of N 2 on W(110) as a benchmark. AIMD is highly accurate as the surface atoms are explicitly part of the dynamics, but this advantage comes with a large computational cost. The GLO model is much more computationally convenient, but accounts for lattice motion e↵ects in a very approximate way. Results show that, despite its simplicity, the GLO model is able to capture the physics of the system to a large extent, returning dissociation probabilities which are in better agreement with AIMD than static-surface results. Furthermore, the GLO model and the AIMD method predict very similar energy transfer to the lattice degrees of freedom in the non-reactive events, and similar dissociation dynamics. a) These authors contributed equally to this work.