An n-sided cell-based smoothed finite element method (nCS-FEM) for the convective heat transfer in incompressible viscous fluid flow is proposed. The Characteristic-Based-Split (CBS) scheme is used to stabilize the spatial and pressure oscillations of CS-FEM that occur during the process of solving incompressible Navier-Stokes equations. In order to verify the proposed method, several numerical examples (thermal Poiseuille flow between two parallel plates, buoyancy-driven convection in a square cavity, flows in throttling channel with heat transfer, thermal Couette flow between vertical coaxial cylinders, unsteady flow over a circular cylinder with heat transfer), including the cases with analytical solutions, are used to test the accuracy of CS-FEM. Moreover, the investigation of the robustness of highly distorted element is conducted in a natural convection test case. The calculation results of numerical examples show that CS-FEM is qualified to solve the steady and unsteady convective heat transfer problems for incompressible laminar flow with high reliability. Furthermore, the proposed method has been demonstrated to be highly effective and applicable in addressing advanced three-dimensional convective heat transfer engineering problems with remarkable results. The method promises to provide more relevant and practical solutions that will help engineers and scientists tackle the growing challenges faced in various industries.