This paper presents a regularization technique suited to the inverse problem associated with the reconstruction of the internal convection coefficient from external temperature measurements. More precisely, the error function between measured and prospective temperatures, obtained from a prospective convection coefficient, is minimized by applying the Newton method. The Truncated Singular Value Decomposition method is used to regularize the corresponding Hessian matrix. Numerical simulations were performed for three different test cases and three different randomly perturbed initial guesses in order to validate the proposed method. Results confirm that the convection coefficient can be reconstructed within reasonable precision.