Due to the extreme thermal conditions and short lifetimes, experimental exploration of cathode spots in vacuum arcs is very difficult. The intensive heat in the cathode spot is believed to be generated by ion bombardment and by Joule heating. However, thermal conditions occurring inside the re-melted material in craters created by cathode spots are not accurately known. During the exposure to cathodic arc plasmas, an Al-Cr cathode’s surface was locally melted by successive ignition and extinction of cathode spots. The melted layer, that quickly solidified, was characterized by the formation of several thin layers with a thickness of a few micrometers that were stacked on top of each other. The corresponding solidification patterns displayed cellular and dendritic microstructures. A phase field-based model was used to simulate and determine the thermal process conditions that led to the dendritic structures observed within the re-melted layer. Different combinations of cooling rates and temperature gradients were numerical explored to determine the most probable thermal conditions under which the cathode material re-solidifies. The results showed that the material in the vicinity of the cathode spot crater re-solidified under the condition of a cooling rate of about 3 × 105 K/s and a temperature gradient of about 6 × 107 K/m. These results constitute valuable data for the validation of numerical models dedicated to cathode spot formation.