This study presents a radial fin with half elliptical profile and performs a thermal analysis on it. The meshless local Petrov–Galerkin (MLPG) method with a predictor–corrector scheme is used. The function approximation is done using moving least square (MLS) scheme and essential boundary condition is imposed with the penalty method. The results are validated with the available exact solution and was found in good agreement. A parametric study is performed, thereafter, to show variation of temperature and performance of the fin over a range of parameters, namely thermo-geometric parameter, thermal conductivity parameter and convection parameter. Numerical investigation reveals that this profile has a better performance based on the rate of heat transfer from the fin per unit mass of the material used.