Non-equilibrium electron spin relaxation in a n-type doped GaAs bulk semiconductor is investigated. We use a semiclassical Monte Carlo approach by considering multivalley spin dynamics of drifting electrons. Spin relaxation is considered through the D’yakonov–Perel mechanism, which is the dominant process in III–V semiconductors. An analytical expression for the inhomogeneous broadening of spin precession vector is derived by taking into account the effect of the electric field and the doping density. The inclusion of electron–electron scattering has the effect of increasing both the spin lifetime and the depolarization length. In particular, we find a non-monotonic trend with the maximum of both the spin lifetime and the depolarization length, as a function of the lattice temperature. This peculiar behavior, which is due to the nonlinear spin-lattice interaction through the phononic thermal bath, is akin to the noise-enhanced stability phenomenon. Moreover, for lattice temperatures up to 77 K the electron spin lifetime slightly increases with the doping density, while the spin depolarization length shows a decreasing behaviour. For electic field amplitudes higher than the threshold field (Gunn field), the spin lifetime increases with the lattice temperature. Our numerical findings are validated by a good agreement with the available experimental results.