(CoxMn1-x)3O4 is a promising candidate material for solar thermochemical energy storage. A high-temperature model for this system would provide a valuable tool for evaluating its potential. However, predicting phase diagrams of complex systems with ab initio calculations is challenging due to the varied sources affecting the free energy, and with the prohibitive amount of configurations needed in the configurational entropy calculation. In this work we compare three different machine-learning (ML) approaches for sampling the configuration space of (CoxMn1-x)3O4, including a simpler ML approach, which would be suitable for application in high-throughput studies. We use experimental data for a feature of the phase diagram to assess the accuracy of model predictions. We find that with some methods, data pretreatment is needed to obtain accurate predictions due to inherently composition-imbalanced training data for a mixed phase. We highlight that the important entropy contributions depend on the physical regimes of the system under investigation and that energy predictions with ML models are more challenging at compositions where there are energetically competing ground state crystal structures. Similar methods to those outlined here can be used to screen other candidate materials for thermochemical energy storage.