<p>In materials simulations, formation energies can provide valuable information about the stability of different crystal polymorphs. However, at finite temperatures, it is often essential to go beyond simple energetics and include free energies in the analysis, as many crystal phases are stabilized by entropic contributions. Therefore, solid-solid phase transitions at finite temperatures are common. Traditionally, free energies of crystalline solids are computed through an analysis of the phonon band structure, which is calculated within the harmonic approximation considering only the crystalline unit cell and its periodic replications. Configurational contributions to the free energy are typically only taken into account for systems such as high-entropy alloys, where the multiplicity can be calculated analytically. We present a numerical approach for calculating configurational entropy that is applicable to essentially any system. By a combination of machine-learned interatomic potentials and efficient structure search methods, we are able to obtain a huge number of inherent structures and study their influence on the free energy of the system. To obtain these structures, it is necessary to generate large periodic cells that can represent not only the perfect crystalline structure but also a very large number of defective structures. Reliable estimates of phase transition temperatures can only be obtained if the configurational density of states is well converged with respect to this cell size. We illustrate this effect for lithium alanate, where the configurational entropy contribution of the structurally tolerant ionic phase reduces the transition temperature to the polymeric phase by 150 K.</p>