In this work, we address the question of the influence of magnetic islands on the perpendicular transport due to steady-state ITG turbulence on the energy transport time scale. We demonstrate that turbulence can cross the separatrix and enhance the perpendicular transport across magnetic islands. As the perpendicular transport in the interior of the island sets the critical island size needed for growth of neoclassical tearing modes, this increased transport leads to a critical island size larger than that predicted from considering collisional conductivities, but smaller than that using anomalous effective conductivities. We find that on Bohm time scales, the turbulence is able to re-establish the temperature gradient across the island for islands widths w ≲ λturb , the turbulence correlation length. The reduction in the island flattening is estimated by comparison with simulations retaining only the perpendicular temperature and no turbulence. At intermediate island widths, comparable to λturb , turbulence is able to maintain finite temperature gradients across the island.