  The atmosphere of a hot jupiter may be subject to a thermo-resistive
instability, in which the increasing electrical conductivity with temperature
leads to runaway Ohmic heating. We introduce a simplified model of the local
dynamics in the equatorial region of a hot jupiter that incorporates the back
reaction on the atmospheric flow as the increasing electrical conductivity
leads to flux freezing, which in turn quenches the flow and therefore the Ohmic
heating. We demonstrate a new time-dependent solution that emerges for a
temperature-dependent electrical conductivity (whereas a
temperature-independent conductivity always evolves to a steady-state). The
periodic cycle consists of bursts of Alfven oscillations separated by quiescent
intervals, with the magnetic Reynolds number alternating between values smaller
than and larger than unity, maintaining the oscillation. We investigate the
regions of pressure and temperature in which the instability operates. For the
typical equatorial accelerations seen in atmospheric models, we find
instability at pressures $\sim 0.1$--$1\ {\rm bar}$ and temperatures $\approx
1300$--$1800\ {\rm K}$ for magnetic fields $\sim 10\ {\rm G}$. Unlike previous
studies based on a constant wind velocity, we find that the instability is
stronger for weaker magnetic fields. Our results add support to the idea that
variability should be a feature of magnetized hot jupiter atmospheres,
particularly at intermediate temperatures. The temperature-dependence of the
electrical conductivity is an important ingredient that should be included in
MHD models of hot jupiter atmospheric dynamics.
