Normally heating causes melting and not solidification. Here we describe a fundamental series of experiments in which heating a reactive porous medium from above leads to crystallization in the interior. As the porous matrix near the heated boundary dissolves, the resulting dense interstitial liquid sinks into the cooler porous matrix, becomes supersaturated and recrystallizes. We present a theoretical model that quantifies how this vertical redistribution of composition leads to the formation of layers in an initially homogeneous porous medium. We propose that this is a fundamental and naturally occurring process in a variety of different situations in permeable rocks.