Phase-change random-access memory relies on the reversible crystalline-glassy phase change in chalcogenide thin films. In this application, the speed of crystallization is critical for device performance: there is a need to combine ultrafast crystallization for switching at high temperature with high resistance to crystallization for non-volatile data retention near to room temperature. In phase-change media such as nucleation-dominated Ge2Sb2Te5, these conflicting requirements are met through the highly fragile nature of the temperature dependence of the viscosity of the supercooled liquid. The present study explores, using ultrafast-heating calorimetry, the equivalent temperature dependence for the growth-dominated medium Ag-In-Sb-Te. The crystallization shows (unexpectedly) Arrhenius temperature dependence over a wide intermediate temperature range. Here it is shown that this is evidence for a fragile-to-strong crossover on cooling the liquid. Such a crossover has many consequences for the interpretation and control of phase-change kinetics in chalcogenide media, helping to understand the distinction between nucleation- and growth-dominated crystallization, and offering a route to designing improved device performance.