We employ analytical and numerical techniques to examine a phase tran-sition model with moving boundaries. The model displays two relevant spatial scales: amacroscopic scale which governs the overall heat conduction inside the dominant phaseand a microscopic scale consisting of small inclusions of a second phase which may shrinkor grow. We use the Hanzawa transformation to transform the problem onto a fixed reference domain and utilize a Schauder fixed-point argument to demonstrate the well-posedness of this system for a finite time interval. Due to the model’s nonlinearities andthe macroscopic parameters, which are given by differential equations that depend onthe size of the inclusions, the problem is computationally expensive to solve numerically.We introduce a precomputing approach that solves multiple cell problems in an offlinephase and uses an interpolation scheme afterwards to determine the needed parameters.Additionally, we propose a semi-implicit time-stepping method to resolve the nonlinearityof the problem. We investigate the errors of both the precomputing and time-steppingprocedures and verify the theoretical results via numerical simulations.