Directional solidification occurs in industrial and natural processes, such as freeze-casting, metal processing, biological cryopreservation and freezing of soils. Translational temperature gradient stage allows to control the process of directional solidification and to visualize it with optical microscope. In this stage freezing velocity and temperature gradient are decoupled and are independently controlled. Here we study the dynamics of the phase transition interface in thin water samples using translational temperature gradient stage. We follow position of the ice–water interface with optical microscopy and compare it to solution of one dimensional Stefan problem in the low velocity limit. We find an agreement between experimental observations and theoretical predictions for constant velocity and during acceleration of the ice front. This work presents a practical framework for analysis and design of experiments on a translational temperature gradient stage.