In this paper, based on the hyperbolic equation of heat conduction, utilizing the image method and the wave function expansion method, the temperature distributions on the surface of a functionally graded material(FGM) containing a cylindrical inclusion are investigated. According to the model of thermal waves, a general solution of scattered fields of thermal waves is obtained. Effects of different physical parameters (such as the depth of buried inclusion, the thermal conductivity, the thermal diffusion length, the thermal diffusivity, and the thermal relaxation time) on the distribution of temperature are analyzed. The thermal waves are excited on the surface of the FGM by a periodically modulated laser. A cylindrical defect is taken as an inclusion under a thermal conduction condition. Results are expected to provide calculation methods and reference data for infrared thermal wave nondestructive evaluation of an FGM and the inverse problems in mathematical physics.