Finite element solutions are highly sensitive to the finite element shape selected and the number of nodes. In this study, a new higher-order finite element analysis is employed to investigate the non-axisymmetric thermoelastic performance of a hollow cylinder made of functionally graded material (FGM) exposed to variable hoop temperature. The analysis employs higher-order finite triangular elements with 6- and 10-nodes to increase the accuracy of the numerical solution as it deals with a curve shaped problem. A strong agreement was achieved when a comprehensive comparison of the thermal and displacement distributions across the cylinder's annulus was conducted with analytical and numerical solutions from prior literature. This study also examines the impact of the volume-graded index on heat and displacement variations along the radial direction. This investigation contributes to understanding the thermal stresses in FGM and highlights the effectiveness of finite element method in analyzing complex thermoelastic systems.