[en] The purpose of this paper is to study the relaxation of the velocity distribution of low-energy electrons cooled or heated by the rotational excitation or de-excitation of nitrogen molecules with many more rotational energy levels than two by using the Monte Carlo simulation in the system where the electrons are so diluted in the heat-bath molecules that the effect of the electron-electron collision is negligible as compared with that of the electron-molecule collision. This paper investigates whether the electrons maintain the initial Maxwell distribution in the cooling process, which corresponds to the cross-modulation experiment, or in the heating process, which corresponds to the shock-wave heating, and the electron temperature obeys that of Mentzoni and Row for the local Maxwell distribution. The author attempts to find out whether the initial S-function velocity distribution, being far from the Maxwell distribution, actually approaches the Maxwell distribution through the rotational excitation and de-excitation only