A new kind of instability caused by Joule heating near charge-selective surfaces (permselective membranes, electrodes, or systems of micro- and nanochannels) is investigated theoretically using a model based on the Rubinstein-Zaltzman approach. A simple relation is derived for the marginal stability curves: Joule heating can either destabilize or stabilize the steady state, depending on the location of the space charge region relative to the gravity vector. For the destabilizing case, the short-wave Rubinstein-Zaltzman instability is replaced by a long-wave thermal instability. The physical mechanism of the thermal instability is found to be very different from Rayleigh-Bénard convection, and is based on a nonuniform distribution of the electrical conductivity in the electrolyte. The study is complemented by numerical investigations both of linear and nonlinear instabilities near a charge-selective surface. There is a good qualitative agreement with the analytics. A possible explanation of the discrepancy between the experimental data and our previous theoretical voltage-current characteristics is highlighted.