The plane strain problem for a functionally graded solid cylinder with thermal energy generation under the effect of convective heat transfer is considered. In previous studies on FGM cylinders in the literature, the modulus of elasticity, the thermal conductivity and the thermal expansion coefficient are represented by using either exponential or power functions. However, this study considers different functions for these material properties, which results in a more realistic representation of the problem. The stress and strain components are evaluated analytically and their dependencies on the radially varying material parameters are presented at the elastic state. Critical values of the volumetric thermal energy generation evaluated for a homogeneous solid cylinder and for an FGM cylinder are compared by using the Tresca's Yield Criterion. Numerical results are generated by considering a W/Cu FGM solid cylinder which has potential applications as an International Thermonuclear Experimental Reactor (ITER) component.