Functionally graded materials are renowned for minimizing abrupt stress transitions typical of laminated composites. They are highly suitable for operation in adverse high-temperature environments and can act as thermal barriers, especially when considering a proper selection of constituent materials. While these materials have been the subject of intense research by the scientific community, existing studies have predominantly focused on rectangular cross-section beams or plates. Beams with different cross-section profiles can also benefit from the continuous smooth material transition of functionally graded materials, particularly when subjected to thermal loads. Therefore, this study explores the influence of functionally graded materials on the harmonic behavior of symmetrical I-beams. The investigation involves a parametric analysis using the thermoelastic model. The beams undergo harmonic loading and thermal variations, with subsequent study of the resulting spectra and stress distributions. As anticipated, the material mixtures influence both harmonic behaviors and stress profiles.