SiC thermal conductivity is known to decrease under irradiation. To numerically model this effect, we studied the variation of the thermal conductivity of cubic SiC with the defect accumulation induced by displacement cascades. We use empirical potential of the Tersoff type in the framework of non-equilibrium molecular dynamics. The conductivity is found to decrease with dose in very good quantitative agreement with low temperature irradiation experiments. The results are analyzed in view of the amorphization states that are created by the cascade accumulation simulations. The decrease of the conductivity observed at lower doses is related to the creation of point defects. The calculated values are close to the smallest measured values after high temperature irradiation. A subsequent decrease takes place upon further cascade accumulation. It is characteristic of the amorphization of the material and is experimentally observed for low temperature irradiation only.