In this paper we study the temperatures of electrons convected with the solar wind to large solar distances and finally transported over the solar wind termination shock. Nearly nothing, unless at high energies in the cosmic ray regime, is known about the thermodynamical behaviour of these distant electrons from in~situ plasma observations. Hence it is tacitly assumed these electrons, due to their adiabatic behaviour and vanishing heat conduction or energization processes, have rapidly cooled off to very low temperatures once they eventually arrive at the solar wind termination shock (at about 100 AU). In this paper we show that such electrons, however, at their passage over the termination shock due to the shock–electric field action undergo an over-adiabatic heating and therefore appear on the downstream side as a substantially heated plasma species. Looking quantitatively into this heating process we find that solar wind electrons achieve temperatures of the order of 2–4 × 10⁶ K downstream of the termination shock, depending on the upstream solar wind bulk velocity and the shock compression ratio. Hence these electrons therewith play an important dynamical role in structuring this shock and determining the downstream plasma flow properties. Furthermore, they present an additional ionization source for incoming neutral interstellar hydrogen and excite X-ray emission. They also behave similar to cosmic ray electrons and extend to some limited region upstream of the shock of the order of 0.1 AU by spatial diffusion and thereby also modify the upstream solar wind properties.