Renewed interest in additive manufacturing (AM) and rapid prototyping technologies has driven great demand for corresponding modeling and simulation tools. While most such models are defined via the finite-element discretization of the relevant multi-physics, the authors have recently developed a method based on the enrichment of classical analytic solutions to the heat equation. The principal advantage of this enriched analytic solution methodology (EASM) is its high computational efficiency that can enable in-the-loop process control in a manner that removes assumptions made for classic analytical solutions and accounts for additional physics. These features enable the efficient and accurate exploration of the high-dimensional AM process parameter space. This work presents a further enrichment of the underlying analytic solutions to include the effects of phase transformation upon melting and solidification, which are shown to be significant in magnitude. It is demonstrated that the available property data for common AM materials are not adequate for accurate thermal modeling (via finite-element, EASM, or other means), and must be improved via future experimental efforts. A discussion of the accuracy and significance of the results achieved, and a summary of further work necessary to bring the EASM to maturity concludes this work.