In this paper, we delve into a coefficient inverse problem linked to the bioheat equation, a pivotal component in medical research concerning phenomena such as temperature response and blood perfusion during surface heating. By considering factors like heat transfer between tissue and blood in capillaries and incorporating the geometric intricacies of the skin, we confine our analysis to a one-dimensional domain. Our approach involves transforming the original problem into one concerning the reconstruction of a multiplicative source term within a parabolic equation. Subsequently, we utilize integral conditions to derive a specific integro-differential equation, accompanied by the requisite initial and boundary conditions. Leveraging a spectral method, we streamline the modified problem into a linear system of algebraic equations. To accomplish this, we employ appropriate regularization algorithms to obtain stable approximations for the derivatives of perturbed boundary data and to effectively solve the resultant system of equations.
