For supplying massive liquid water to the outflow channels, igneous melting of the permafrost layer could have played a significant role. We numerically simulate the melting process of the permafrost layer induced by magmatic intrusion. The point of our simulation is incorporation of thermal convection in porous media, which has not been modeled well in previous studies of the melting of the permafrost. Our results show that convection in the melted zone causes drastic change in heat transfer, which results in focusing in the growth of the melt region and enhancement of water generation. The resulting melt zone extends vertically up just next to the surface, like a plume with a single column (mushroom structure). The volume of meltwater is considerably more than that expected in the conduction case. These characteristics suggest that a substantial amount of water may exist very near the surface. In response to compaction, segregated liquid water may have erupted out of the ground to form the fluvial features. Such an event would certainly be accompanied by surface destruction, which we can see as chaotic terrain. We propose a consistent scenario of forming surface features around the outflow channels.