The thermal conductivity of the (2+1)-dimensional NJL model in the presence of a constant magnetic field is calculated in the mean-field approximation and its different asymptotic regimes are analyzed. Taking into account the arising of a quasiparticle gap due to the magnetic catalysis phenomenon, it is shown that for certain relations among the theory's parameters (quasiparticle width, temperature and magnetic field), the profile of the thermal conductivity versus the applied field exhibits kink and plateau-like behaviors. We point out possible applications to planar condensed matter.