## 1 Introduction  
The physics of transient heat transfer allows one to evaluate the dynamics of energy movements for bodies subjected to changes in temperature, enabling the analysis of the heat flux, temperature history, and temperature rate of different processes. Transient heat transfer problems have significant applications in food processing [1, 2], alternative energies [3, 4], oil and gas [5], metallurgical processes [6, 7], metallography [8, 9], infrastructure materials [10, 11], and electronics and semiconductor cooling [12, 13, 14], among others. These applications require analysis of multiple parameters, e.g., time-dependent boundary conditions [15], temperature-dependent thermo-mechanical properties [16, 17], and evolving geometries [18] to guide the design of components. Experimental, analytical, and numerical approaches have been proposed to model transient heat transfer processes. In the experimental approach, level values of the inputs are set to generate random and independent experimental runs. This approach allows the empirical models to capture the dynamic characteristics of a thermal problem regardless of its complexity [19]. It has been used to optimize operational parameters of radiation heat exchange materials [20], induction heating [21], heat treatments [22], sensor design and calibration [23; 24], cooling devices [25; 26], and electronics refrigeration [27]. However, when the processes of interest involve many parameters, and the factors are prone to uncontrollable changes (e.g., uncontrolled room conditions), the experimental approach becomes time-consuming and expensive, limiting its application. Approximations for specific processes can be obtained using simplified analytical solutions for the heat diffusion equation for plates [28], walls [29], cylinders [30; 31], or spheres [32] under temperature, heat flux, or periodic heating [29]. For instance, predictions in the thermal profile of a plate due to a moving heat source can be approximated by this method [33]. However, explicit analytical solutions are uncommon when systems are large, complex, and time-dependent. The approximations based on simplified models lead to significant errors. As a result, numerical models such as the finite element method (FEM), finite-difference methods, and boundary element methods are popular for solving transient heat transfer problems due to their flexibility and versatility. These numerical methods have been used to approximate the solution of the heat diffusion equation in large and complex problems such as the analysis of fractal piping design [34], phase change materials [35], enhanced surfaces [36], heat exchangers [37], heat sinks [38] and additive manufacturing [39; 40], among others. In addition, these and other numerical techniques have been used to study the rate of change of temperature to time in crystallization [2; 41], microstructural evolution [42], and superconducting devices [43]. Regardless of the modeling technique, the more elaborate the model, the more challenging it is to track the effects of the input variables on the outputs of the models. Sensitivity analysis is a technique to determine the interactions among the input parameters in a model. For instance, an output could be insensitive to a specific input but highly sensitive to a combination of that input with other parameters in the model. Sensitivity analysis is also used to quantify the influence of these parameters on the model response [44]. In sensitivity analysis, each of the inputs is represented by sensitivity coefficients given by the partial derivative of the output of interest with respect to each input [19; 23; 24; 45; 46; 47; 48; 49; 50]. The traditional methods to obtain sensitivities are hand-coded analytical differentiation [44], symbolic differentiation [51], automatic differentiation [52], and finite differentiation (FD) [44]. Hand-coded analytical and symbolic differentiation are similar methods as both are exact and rely on analytical models.