  By constructing and numerically solving the kinetic Bloch equations we
perform a many-body study of the spin dephasing due to the D'yakonov-Perel'
effect in $n$-typed GaAs (100) quantum wells for high temperatures. In our
study, we include the spin-conserving scattering such as the electron-phonon,
the electron-nonmagnetic impurity as well as the electron-electron Coulomb
scattering into consideration. The dephasing obtained from our theory contains
not only that due to the effective spin-flip scattering first proposed by
D'yakonov and Perel' [Zh. Eksp. Teor. Fiz. {\bf 60}, 1954(1971)[Sov. Phys.-JETP
{\bf 38}, 1053(1971)]], but also the recently proposed many-body dephasing due
to the inhomogeneous broadening provided by the DP term [Wu, J.
Supercond.:Incorp. Novel Mechanism {\bf 14}, 245 (2001); Wu and Ning, Eur.
Phys. J. B {\bf 18}, 373 (2000)]. Our result agrees with the experiment data
[Malinowski {\em et al.}, Phys. Rev. B {\bf 62}, 13034 (2000)] very well. We
further show that in the case we study, the spin dephasing is dominated by the
many-body effect.
