The projected impact of radiation on semiconductors allows to create on their basis the various elements of sensor electronics with the necessary characteristics, in particular the semiconductor Hall sensors. Therefore, the studies of irradiation by different flows of fast electrons with the energy of 12 MeV on the magnetic sensitivity of n-Si <P> single crystals have been carried out by us. The measurements of Fourier infrared spectroscopy and Hall effect with the aim of identifying the nature of created radiation defects have been conducted. On the basis of the research, it has been established that the main radiation defects, formed in silicon at the electron irradiation, are Ci Oi complexes, A-centers (VOi complexes), and A-centers, which are additionally modified by phosphorus impurity (VOi P complexes). Taking into account the obtained temperature dependencies of the Hall constant, the values of the coefficients of the magnetic sensitivity for unirradiated and irradiated samples of silicon were calculated. The performed calculations show that the magnetic sensitivity of n-Si single crystals increases and significantly depends on a temperature with the increasing of the flow irradiation. A significant increase of the magnetic sensitivity at the temperatures T≈170 K for the largest electron flow 2·1017 el./cm2 (more than 500 times) in relation to unirradiated n-Si <P> single crystals is obtained. The reason for such an increase in the magnetic sensitivity of n-Si <P> is the formation of Ci Oi , VOi and VOi P complexes that create deep energy levels in the band gap of silicon. Such levels act as compensating centres in relation to the main charge carriers. The increase of the degree of compensation of n-Si <P> single crystals with the increasing of the flow of electron irradiation leads to an increase of Hall constant, and hence of the magnetic sensitivity. The obtained results can find a practical application for designing based on of irradiated n-Si <P> single crystals the Hall sensors, which can function in a wide range of temperatures.