The ability to predict and understand phases in high-entropy alloys (HEAs) is still being debated, and primarily true predictive capabilities derive from the known thermodynamics of materials. The present work demonstrates that prior work using high-throughput first-principles calculations may be further utilized to provide direct insight into the temperature- and composition-dependent phase evolution in HEAs, particularly Al-containing HEAs with a strengthening multiphase microstructure. Using a simple model with parameters derived from first-principles calculations, we reproduce the major features associated with Al-containing phases, demonstrating a generalizable approach for exploring potential phase evolution where little experimental data exists. Neutron scattering, in situ microscopy, and calorimetry measurements suggest that our high-throughput Monte Carlo technique captures both qualitative and quantitative features for both intermetallic phase formation and microstructure evolution at lower temperatures. This study provides a simple approach to guide HEA development, including ordered multi-phase HEAs, which may prove valuable for structural applications.