Pattern formation via nonequilibrium dynamical paths has been the focus of much recent attention. An example is phase separation under the action of a nonstationary temperature field. Under directional quenching (DQ), where a region at some “quenched” temperature spreads in one direction over time, it has been found that a variety of patterns (random droplet, lamellar, and columnar patterns) may be formed by controlling the dynamics of the quenching front in two dimensions. Although a similarly rich phenomenology may be expected in three dimensions (3D), DQ in 3D would require temperature control in bulk, which is difficult to realize. Instead of DQ, we fix the temperature gradient through the slab, and control of the surface temperature of both sides of the slab (gradient cooling, GC). It seems similar to DQ and it is significantly easier to realize experimentally. Here, we compare the mechanism of the phase separation in DQ with that in GC. It is found that no columnar pattern is formed in GC. It is also revealed that a pattern formation mechanism in GC is clearly different from conventional DQ.