The aim of this work is to investigate the time fractional thermoelastic state of a thermally sensitive functionally graded thick hollow cylinder subjected to internal heat source. Convection boundary conditions are applied on the curved surface of cylinder also sectional heating is assumed on the lower surface. The material properties except density and Poisson’s ratio are assumed to be dependent on temperature. Kirchhoff’s variable transformation is used to reduce the nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity to linear form. Further the solution of linear form is obtained by using integral transform technique in the form of Bessel’s and trigonometric functions. All physical and mechanical quantities are taken as dimensional for the theoretical analysis whereas for numerical computations non-dimensional parameters are assumed. Numerical results of temperature change and stress distribution are illustrated graphically for ceramic-metal-based functionally graded materials and shown in figures with the help of Mathematica software.