We have studied the possibility that the electron heating that has been observed in the high-latitude E region during disturbed periods is produced by low-frequency broadband waves of the type that is measured on rockets. We have found that low-frequency waves can be responsible for the observed electron temperature enhancements if a significant portion of the large amplitude waves does not have a wave vector exactly perpendicular to the magnetic field, but rather if their wavevector is a few (2--5) degrees away from perpendicularity. We show that this aspect angle constraint is present because in order to heat the electrons efficiently with low-frequency waves in the magnetized E region we need a large enough component of the perturbed electric field in the magnetic field direction. While aspect angles that are larger than expected from classical linear theory have been detected at times, we propose that they should be limited to low-frequency gradient drift waves. For such waves nonlocal effects are probably strong enough to force the waves to be less field aligned than originally expected. Finally a direct implication of our findings is that a heating mechanism similar to the one discussed in the present paper may produce detectable effects in the equatorial E region during strong electrojet conditions.