The nonlocal theory was first introduced by Eringen. In classical theory, once the strain field at a point is known, the stress state at that same point can be determined through constitutive relations. However, in nonlocal theory, determining the stress at a point requires knowledge of the strain field across the entire domain. In this regard, only limited studies have examined the influence of Eringen’s nonlocal parameter on the vibration analysis of non prismatic columns. The present study investigates the combined effects of Eringen’s nonlocal parameter and the thermal gradient coefficient on the natural frequency of a non prismatic column. Variations in the column’s moment of inertia along its length are considered in three forms: linear, cubic, and fourth order. A finite element method based on sixth order Lagrange shape functions is employed to solve the governing equation. The advantage of this method over conventional finite element procedures is that it eliminates the need for assembling stiffness matrices. Compared to the standard cubic finite element method, the proposed approach offers higher accuracy, faster convergence, improved numerical stability, and efficient implementation in MATLAB. The results indicate that increasing Eringen’s nonlocal parameter and the thermal gradient coefficient may either decrease or increase the dimensionless natural frequency, depending on the boundary conditions. To enhance the practical applicability of the findings and facilitate use by engineers and designers, curve fitting techniques with third degree polynomial functions are employed for formulation. A satisfactory agreement is observed between the results of this study and previous research.