This work aims to study the influence of fractional derivatives and thermal relaxation time on two-dimensional biological tissues using an eigenvalue-based approach. Understanding the heat transfer mechanism and its thermomechanical interactions with the skin tissue of patients is cru cial for the successful implementation of thermal treatment procedure. The study employs Laplace and Fourier transforms, and the resulting formulations are applied to human tissues un dergoing regional hyperthermia treatment for tumor therapy. The numerical inversion process for Laplace and Fourier transformations utilizes the Stehfest numerical inverse method. The re sults demonstrate that thermal relaxation time and fractional order parameter significantly influ ence all analyzed distributions. The numerical findings suggest that thermo-mechanical waves propagate through the skin tissue over finite distances, which helps mitigate the unrealistic pre dictions made by the Pennes' model.