Numerical models for the transient thermal behavior of the interface between a hydrocarbon combustor and the hot end of a Stirling engine have been developed. This interface is a volume comprised of a phase change thermal storage media. One of the models developed is a first order model that permits rapid assessment of the effects of combustor size, thermal storage media size, the presence, and the types of heat transfer surfaces on the overall efficiency of the energy conversion process. The other model is a more advanced transient multidimensional model that couples a computational fluid dynamics simulation of the reacting flow within the combustor to the enclosing combustor and then to the phase change thermal storage volume. The two-phase behavior of the thermal storage media is modeled as well. This model enables an assessment of the best placement of heat transfer surfaces with in the thermal storage material. The application for this system is as a power and energy system for an unmanned undersea vehicle. A principal benefit illustrated by the models is that very rapid thermal charging (i.e. melting) of the energy storage material can occur at the surface that enables a very long duration cruise on the stored energy underwater.