There is a growing interest in cryogenic calorimeters with macroscopic absorbers for applications such as dark matter direct detection and rare event search experiments. The physics of energy transport in calorimeters with absorber masses exceeding several grams is made complex by the anisotropic nature of the absorber crystals as well as the changing mean free paths as phonons decay to progressively lower energies. We present a Monte Carlo model capable of simulating anisotropic phonon transport in cryogenic crystals. We have initiated the validation process and discuss the level of agreement between our simulation and experimental results reported in the literature, focusing on heat pulse propagation in germanium. The simulation framework is implemented using Geant4, a toolkit originally developed for high-energy physics Monte Carlo simulations. Geant4 has also been used for nuclear and accelerator physics, and applications in medical and space sciences. We believe that our current work may open up new avenues for applications in material science and condensed matter physics.