We report observations of coherent elastic and rotationally inelastic scattering of N-2, O-2, and CH4 from a 10 K Cu(111) surface, kept clean by pulsed laser heating. The related sharp features in the measured angular distributions decrease drastically in intensity at elevated target temperatures. At low temperature rotational transitions reduce the elastic scattering probability by about an order of magnitude. This effect is weak for D-2 at the impact conditions of concern. Quantum scattering calculations for N-2 and D-2 show that this difference is primarily caused by the large difference in rotational constants and the associated rotational transition energies of these molecules.