  Hot jupiter atmospheres may be subject to a thermo-resistive instability
where an increase in the electrical conductivity due to ohmic heating results
in runaway of the atmospheric temperature. We introduce a simplified
one-dimensional model of the equatorial sub-stellar region of a hot jupiter
which includes the temperature-dependence and time-dependence of the electrical
conductivity, as well as the dynamical back-reaction of the magnetic field on
the flow. This model extends our previous one-zone model to include the radial
structure of the atmosphere. Spatial gradients of electrical conductivity
strongly modify the radial profile of Alfv\'en oscillations, leading to
steepening and downwards transport of magnetic field, enhancing dissipation at
depth. We find unstable solutions that lead to self-sustained oscillations for
equilibrium temperatures in the range $T_\mathrm{eq}\approx 1000$--$1200$~K,
and magnetic field in the range $\approx 10$--$100$~G. For a given set of
parameters, self-sustained oscillations occur in a narrow range of equilibrium
temperatures which allow the magnetic Reynolds number to alternate between
large and small values during an oscillation cycle. Outside of this temperature
window, the system reaches a steady state in which the effect of the magnetic
field can be approximated as a magnetic drag term. Our results show that
thermo-resistive instability is a possible source of variability in magnetized
hot jupiters at colder temperatures, and emphasize the importance of including
the temperature-dependence of electrical conductivity in models of atmospheric
dynamics.
