Using a nozzle‐type molecular beam with highly uniform velocity and high intensity and a sensitive time‐of‐flight detection system allows the measurement of the complete distribution of speeds after scattering the incident beam from a solid surface. With a ``dirty'' metal target at room temperature and argon as beam gas, it is found that the thermal spread of velocities in the scattered beam is at least three times larger than the thermal spread of velocities in the incident beam. While a complete thermal accommodation of the incident atoms would result in the same speed distribution for all scattering angles, the measurements show an angular dependence of the thermal spread and the mean speed of the scattered atoms.