Thermal energy storage systems utilizing metallic phase change materials exhibit great potential as a technology for mobile applications, offering high storage densities and high thermal discharge rates. First experimental investigations show the functionality and performance characteristics of this system. For a deeper understanding of the thermal discharge, this paper presents a numerical model and analysis of the transient conjugate heat transfer. For validation of the numerical model, the results of the simulations are compared to the available experimental data. The investigated storage is based on an aluminum silicon alloy and a box-shaped graphite container design. In this system, heat extraction is achieved by forced convection of ambient air. The transient thermal discharge was simulated from 650 °C to 100 °C, and the solidification of the storage material at around 577 °C was simulated using an enthalpy-porosity approach. The discharge time and total heat flow show good agreement with the experimental data, indicating the model’s successful validation. An empirical study was carried out to determine the thermal contact resistance at the interface between the storage material and the graphite container. The present study contributes new physical insights regarding the thermal discharge of a novel metallic latent heat thermal energy storage system.