Investigations of designs with a flowing free-surface molten salt as a first wall in the Advanced Power Extraction (APEX) Program led to questions concerning the liquidus temperature and solidification processes for the [1:1:1] composition in the LiF, BeF2 and NaF system. Sandia experiments, reported in this conference, showed a liquidus temperature near 425°C for the [1:1:1] composition. We also identified other compositions that showed congruent (eutectic) solidification and had sufficiently low melting temperatures (~305-320°C) to be useful in this application. Further characterization of these materials is necessary to evaluate their potential. This paper summarizes a 3-D finite element analysis of the experiment that evaluates thermal gradients in the salt pool and crucible, reproduces the "thermal plateau" associated with the isothermal freezing of a eutectic, and compares the calculated temperatures with readings from the three thermocouples in the experiment.