Electrodynamics plays an important role in controlling circulation and energy balance in Saturn's auroral thermosphere, but less is known about its effects at lower latitudes. Recent observations by the Cassini magnetometer instrument, taken around the equator during the Grand Finale tour, revealed azimuthal magnetic field perturbations of the order of 10-30 nT associated with electrodynamics in Saturn's upper atmosphere. In order to investigate the implications of these observations, we develop a steady-state, axisymmetric model adapted from terrestrial studies to simulate wind-driven electrodynamics at low to middle latitudes in Saturn's thermosphere. Our results demonstrate, based on rigorous theory, that the magnetic field observations can be reproduced by a wind dynamo generating electric currents in the ionosphere of the order 10-9 - 10-7 Am-2 provided that eastward zonal winds of the order of 100 ms-1 exist in the equatorial thermosphere. The resistive (Joule) heating rate based on the equatorial current system, however, is significantly lower than that required to explain the temperatures in Saturn's thermosphere. In spite of this, we find that resistive heating and ion drag due to a mid-latitude wind dynamo have the potential to alter the energy balance and general circulation in Saturn's thermosphere and should be treated self-consistently in future global circulation models.