An investigation has been conducted to examine the complexities associated with the thermal performance of a nonlinear problem pertaining to the porous fin characterized by temperature-dependent internal heat generation. It is posited that the heat generation is contingent upon temperature. The impacts of the natural convection parameter Nc, internal heat generation "g, porosity Sh, and generation number G on the dimensionless temperature distribution are thoroughly examined. A novel intelligent computational strategy is established for solution identification. To achieve this objective, the governing equation is reformulated into a corresponding problem with boundary conditions conducive to the application of a modified version of Chebyshev polynomials of the first kind. The functions based on these Chebyshev polynomials generate an approximate series solution with undetermined weights. The mathematical optimization framework comprises an unsupervised error, minimized by adjusting weights through the interior point method. The proposed approximate solution is corroborated by enforcing tolerance constraints within the optimization framework.