<p>The article’s goal is to introduce a nonlocal heat conduction mathematical model that forecasts tissue temperature during thermal ablation with temperature dependent thermal conductivity. The motivation for solving such problems lies in the need for more accurate, effective, and personalized treatment planning. By incorporating nonlocal effects and accounting for temperature-dependent properties, the model becomes more reflective of the actual heat distribution in tissues, leading to better predictions of tissue damage, improved patient outcomes, and more efficient use of medical resources. To solve the problem Kirchhoff’s transformation is used which simplifies the governing bioheat transfer equation. A finite difference strategy has been used to discretize the problem numerically in space coordinates; the finite element Legendre wavelet Galerkin method (FELWGM) is used to solve the reduced system of ordinary differential equations. To assess the impact of varying thermal conductivity on tissue temperature distribution for various physical factors, a parametric analysis is conducted and graphically represented. Additionally, particular cases are inferred from the current study. There is a thorough discussion of how the generalized coordinate system, lagging time, external heat source coefficient, temporal variability, nonlocal parameter, and thermal conductivity parameter variations affect tissue temperature. This approach helps optimize thermal ablation therapies and ensures a higher degree of precision in targeting and treating abnormal tissue, while minimizing harm to surrounding healthy tissues.</p>