This paper presents experimental data from a two-layer test sample made up of a copper layer and an AISI type 316 stainless steel (SS) layer that was heated with a laser power source. Experiments were conducted to generate high-temperature benchmark data that ranged from room temperature to 820 °C. The concept of time rescaling was employed to account for the dependence of thermal diffusivity on temperature in order to utilize the calibration integral equation method (CIEM). The future time regularization method was used to obtain a stable prediction for the surface temperature. An estimate for the future time regularization parameter was acquired through analysis of the in-depth calibration test thermocouple (TC) response. Results for three test cases consisting of selected pairs of calibration data and reconstruction data (to be predicted) are presented and discussed. Four different values of the future time regularization parameter were employed in the three test cases. The proposed nonlinear (NL) formulation improved the prediction accuracy when compared to the constant properties formulation of the CIEM. It should be emphasized that no knowledge of TC probe depth or TC response properties is required.