Measurements of spin dynamics of electrons in high-mobility, two dimensional electron gases (2DEGs) in GaAs/AlGaAs quantum wells from 5K to 300K show a rapid increase of spin relaxation time up to a peak near the Fermi temperature. Theoretical analysis based on the D'yakonov-Perel' mechanism shows that this variation is 'motional slowing' caused by electron-electron scattering and that the mobility of the electrons plays a minor role in the spin dynamics.