This work presents an experimental and straightforward procedure for the simultaneous estimation of temperature-dependent thermophysical properties of metallic materials. Thermal conductivity, k, and specific heat, c_p, of a 304 stainless steel metal sample are obtained. The thermal model is based on three-dimensional, transient and nonlinear heat conduction across a metal slab, which is partially heated by a constant heat flux on the upper side, and insulated on the other surfaces. The contact resistance effect caused by the imperfect contact between the heater and the sample is considered a reducing factor on the heat flux delivered to the metal. This helped addressing a more realistic thermal analysis, increasing sensitivity and enabling better assess the heat diffusion phenomenon. Prior information about the estimation viability is obtained through sensitivity analysis, which also contributes to establishing all experimental features, such as sensor placement. The best location to collect temperature measurements is determined by D-optimality-based sensitivity analysis, aiming that single thermocouple data provides enough information to identify both thermal properties. The numerical temperature field is calculated in COMSOL Multiphysics from known initial and boundary conditions. The temperature-dependent thermophysical properties are simultaneously evaluated using numerically calculated temperatures compared to transient measurements at room temperature. This inverse heat conduction problem is solved by the Levenberg−Marquardt algorithm. Then, the reliability of the achieved outcomes is confirmed by employing these results in the Nonlinear Function Specification Method to recover the heat flux applied on the experimental procedure. Additionally, a statistical study into the confidence bounds is performed to reveal the quality of the results. Finally, the accuracy of the estimation procedure is examined through the uncertainty analysis deriving from experimental and numerical errors.