The numerical, analytical, theoretical and experimental study of thermal transport is an active field of research due to its enormous applications and use in numerous systems. This report covers the impacts of thermal transport on pseudo-plastic material past over a horizontal, heated and stretched porous sheet. Modeling of energy conservation is based upon a generalized heat flux model along with a heat generation/absorption factor. The modeled phenomenon is derived in the Cartesian coordinate system under the usual boundary-layer approach proposed by Prandtl, which removes the complexity of the problem. The modeled rheology is obtained in the form of coupled, nonlinear PDEs. These derived PDEs are converted into ODEs with the engagement of similarity transformation. Afterwards, converted ODEs containing some emerging parameters have been approximated numerically with a powerful and effective scheme, namely the finite element approach. The obtained results are compared with the published findings as a limiting case of current research, and an excellent agreement in the obtained solution was found, which guarantees the effectiveness of the used methodology. Furthermore, it is recommended that the finite element approach is a good method among other existing methods and can be effectively applied to nonlinear problems arising in the mathematical modeling of different phenomenon.