This research introduces a novel framework integrating stochastic finite element analysis (FEA) with advanced circular statistical methods to optimize heat pump efficiency under material uncertainties. The proposed methodologies and optimization focus on balancing the mean efficiency and variability by adjusting the concentration parameter of the Von Mises distribution, which models directional variability in thermal conductivity. The study highlights the superiority of the Von Mises distribution in achieving more consistent and efficient thermal performance compared to the uniform distribution. We also conducted a sensitivity analysis of the parameters for further insights. The results show that optimal tuning of the concentration parameter can significantly reduce efficiency variability while maintaining a mean efficiency above the desired threshold. This demonstrates the importance of considering both stochastic effects and directional consistency in thermal systems, providing robust and reliable design strategies.