The microstructure of food is key to its sensorial perception, and methods to characterize the microstructure are of crucial importance in food engineering. Ice cream is a special example whose microstructure changes dramatically in response to temperature variations. Since ice cream is a multiphase material, the complex interactions among the phases and the physical mechanisms that drive the evolution of microstructure are not yet well understood. This is mostly due to the fact that observing the microstructure with traditional microscopic methods is destructive and does not allow the study of undisturbed samples. With X-ray micro-tomography, it is possible to overcome these limitations and carry out time lapse studies of the evolution of the microstructure of ice cream. Using iodine as a contrast agent, we measured the three-dimensional distribution of the three main phases (air, unfrozen sugar solution, and ice crystals) with a voxel size of 6 mm. An automated routine was developed that allows for the segmentation of the three phases. Based on the three-dimensional data we calculated the temporal evolution of air bubble sizes and ice crystal sizes during cyclic variations of temperature. Under the given temperature variations we find strong hints that for ice crystal coarsening a melt refreeze mechanism and for air microstructure coarsening coalescence are the dominating underlying mechanisms. This method - which can be applied to a plethora of soft multiphase materials - provides new insights into the coarsening mechanisms of multiphase materials and could contribute to a better understanding of complex materials.