A new method for obtaining spatially resolved electron energy distributions is described and applied to cylindrical bore electric discharges. The method is based on a modified two‐term spherical harmonic expansion of Boltzmann’s equation in which energy‐resolved drift and diffusion are included, as well as Joule heating or cooling by the ambipolar field. It is found that low‐energy electrons may be heated by the large ambipolar electric field gradients near the wall while higher‐energy electrons may escape the plasma. Therefore, diffusion cooling and Joule heating in the ambipolar field may simultaneously occur, but for different portions of the electron energy distribution.