Understanding the atomic-scale mechanisms that govern the structure of interfaces is critical across materials systems but particularly so for two-dimensional (2D) moiré materials. Here, we image, atom-by-atom, the thermally induced structural evolution of twisted bilayer transition metal dichalcogenides using in situ transmission electron microscopy. We observe low-temperature, local conversion of moiré superlattice into nanoscale aligned domains. Unexpectedly, this process occurs by nucleating a new grain within one monolayer, whose crystal orientation is templated by the other. The aligned domains grow through collective rotation of moiré supercells and hopping of 5|7 defect pairs at moiré boundaries. This provides mechanistic insight into the atomic-scale interactions controlling moiré structures and illustrates the potential to pattern interfacial structure and properties of 2D materials at the nanoscale.