<p>Temperature-dependent thermophysical properties lead to nonlinear transient heat conduction problems. This phenomenon is commonly observed in numerous engineering applications. Predicting surface heat flux and temperature variations under these conditions is challenging due to the mathematical and physical complexity of the nonlinear governing equation. To resolve this issue, this paper proposes a calibration integral equation based on the Laplace transform combined with a linearization approach. For one-dimensional nonlinear inverse heat conduction problems with insulated back surface condition, this method effectively achieves surface heat flux estimation with minimal input of system parameters. In the nonlinear heat conduction process, the thermal conductivity and heat capacity are temperature-dependent. However, in case the thermal diffusivity is not highly temperature-dependent, linearization technique can be adopted to simplify the nonlinear heat equation. Under such a condition, both numerical simulations and laser heating experimental results illustrate the accuracy and robustness of the proposed approach. This data-driven methodology offers valuable theoretical support for industrial design and thermal management.</p>