Electric fields map from the magnetosphere to the E region ionosphere where they drive the intense currents of the auroral electrojet. Particularly during geomagnetic storms and substorms, these currents become sufficiently intense to develop Farley‐Buneman (FB) streaming instabilities and become turbulent. This leads to anomalous electron heating which can raise the electron temperature from 300 K to as much as 4000 K and, also, modifies auroral conductivities. This paper describes the first fully kinetic 3‐D simulations of electric field‐driven turbulence in the electrojet and compares the results with 2‐D simulations and observations. These simulations show that 3‐D turbulence can dramatically elevate electron temperatures, enough to explain the observed heating. They also show the saturated amplitude of the waves; coupling between linearly growing modes and damped modes...