This work is an extension of the previous semi-analytical work (Teng et al 2016 Nucl. Fusion56 106001), explaining the density limit with a thermo-resistive tearing mode model. The thermo-resistive island growth is calculated with a 3D MHD code M3D-C1 (Jardin et al 2012 Comput. Sci. Discovery5 014002). It is shown with nonlinear 3D MHD simulations that impurity radiation stimulates large magnetic islands at the density limit. The impact of thermal perturbations inside and outside of the island is explored. Inside the island, net cooling enhances the island growth and net heating suppresses its growth. Outside the island, thermal perturbations have a much smaller impact on the island growth. When the plasma density is increased towards the density limit, the island changes from being heated to being cooled and grows to a much larger island width. The convergence test of the simulations over the temporal and spatial grid is performed. The numerical model and the semi-analytical model are compared by calculating the terms, which are defined in the modified Rutherford equation, and good agreement is observed.