Numerous radar observations demonstrate anomalously strong electron heating in polar electrojets during magnetic storms. The effect correlates with strong convection electric field. Anomalous heating of electrons is caused by turbulent electric fields developing in the E region due to the Farley-Buneman instability. A quantitative model of the effect is proposed. Numerical computations are based on a kinetic code. A good agreement of the theoretical results with the existing observations supports the physical ideas underlying the model.