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Recently, electrical injection of spin polarization in n-type and p-type silicon has been experimentally carried out up to room-temperature. Despite of these preliminary but promising experimental results, a comprehensive theoretical framework concerning the influence of transport conditions on the phonon-induced spin depolarization process in silicon structures, in a wide range of values of temperature, doping concentration and amplitude of external fields, is still in a developing stage. In order to elucidate the electron transport and spin dynamics of conduction electrons in lightly doped n-type Si crystals we have performed semiclassical multiparticle Monte Carlo simulations and numerically calculated the spin lifetimes of drifting electrons heated by the electric field. Spin flipping is taken into account through the Elliot-Yafet mechanism, which is dominant in group IV materials. We discuss the influence of different intravalley and intervalley phonon interactions in the spin relaxation process during the spin transport. Our findings are in good agreement with those obtained by using different theoretical approaches and with the most recent experimental results obtained in spin transport devices. Moreover, our Monte Carlo predictions, in ranges of temperature and field amplitude yet unexplored, can be used as a guide for future experimental studies oriented towards a more effective optimization of room-temperature silicon-based spintronic devices.