Observations by the EISCAT Svalbard radar show that electron temperatures T_e in the cusp electrojet reach up to about 4000 K. The heat is tapped and converted from plasma convection in the near Earth space by a Pedersen current that is carried by electrons due to the presence of irregularities and their demagnetising effect. The heat is transfered to the neutral gas by collisions. In order to enhance T_e to such high temperatures the maximally possible dissipation at 50% demagnetisation must nearly be reached. The effective Pedersen conductances are found to be enhanced by up to 60% compared to classical values. Conductivities and conductances respond significantly to variations of the electric field strength E, and "Ohm's law" for the ionosphere becomes non-linear for large E.