This study presents a novel approach inspired by the hexagonal honeycomb structure found in nature, leveraging image processing algorithms to precisely define complex geometries in thermal systems. Hexagonal phase change material containers and thermally conductive fins were meticulously delineated, mirroring the intricate real-world designs of honeycombs. This innovative methodology not only streamlines setup processes but also enhances our understanding of melting dynamics within enclosures, highlighting the potential benefits of biomimetic design principles in engineering applications. Two distinct honeycomb structures were employed to investigate their impact on the melting process within cavities subject to heating from the left wall, with the remaining walls treated as adiabatic surfaces. The incorporation of a thermally conductive fin system within the enclosure significantly reduced the time required for a complete phase change, emphasizing the profound influence of fin systems on thermal design and performance. This enhancement in heat transfer dynamics makes fin systems advantageous for applications prioritizing precise temperature control and expedited phase change processes. Furthermore, the critical role of the fin system design was emphasized, influencing both the onset and location of the final point of melting. This underscores the importance of tailoring fin systems to specific applications to optimize their performance. Our study highlights the significant impact of the Rayleigh (Ra) number on the melting time in a cavity without fins, revealing a decrease from 6 to 0.4 as the Ra increased from 102 to 105; the introduction of a fin system uniformly reduced the melting time to Ste.Fo = 0.5, indicating fins’ universal effectiveness in optimizing thermal dynamics and expediting the melting process. Moreover, the cavity angle was found to significantly affect the fluid fraction diagram in unfanned cavities but had minimal impact when fins were present, highlighting the stabilizing role of fins in mitigating gravitational effects during melting processes. These insights expand our understanding of cavity geometry and fin interactions in heat transfer, offering potential for enhanced thermal system designs in various engineering applications. Decreasing thermal conductivity (λ) by increasing the fin thickness can halve the melting time, but the accompanying disadvantages include a heavier system and reduced energy storage due to less phase change material, necessitating a careful balance in decision-making.