Analytical first and second-order sensitivities are derived for a general, transient nonlinear problem and are then used to solve an inverse heat conduction problem (IHCP). The inverse analyses use Newton’s method to minimize an error function which quantifies the discrepancy between the experimental and predicted responses. These Newton results are compared to results obtained from the first-order variable metric Broyton-Fletcher-Goldfarb-Shanno (BFGS) method. Inverse analyses are performed for both linear and nonlinear thermal systems. For linear systems, Newton’s method converges in one iteration. For nonlinear systems, Newton’s method sometimes diverges apparently due to a small radius of convergence. In these cases a combined BFGS-Newton’s method is used to solve the IHCP. The unknown data fields are parameterized via the eigen basis of the Hessian to illustrate the need for regularization. Regularization is then incorporated and the IHCP is solved with Newton’s method. All heat transfer analyses and sensitivity analyses are performed via the finite element method.