We report a 2D modeling of the thermal diffusion-controlled growth of a vapor bubble attached to a heating surface during saturated boiling. The heat conduction problem is solved in a liquid that surrounds a bubble with a free boundary and in a semi-infinite solid heater by the boundary element method. At high system pressure the bubble is assumed to grow slowly, its shape being defined by the surface tension and the vapor recoil force, a force coming from the liquid evaporating into the bubble. It is shown that at some typical time the dry spot under the bubble begins to grow rapidly under the action of the vapor recoil. Such a bubble can eventually spread into a vapor film that can separate the liquid from the heater thus triggering the boiling crisis (critical heat flux).