Thermoelastic analysis of functionally-graded nonuniform rotating disks subjected to nonuniform change in temperature essentially requires solutions of two-point-boundary-value problems. Spatial variations of thermomechanical properties, thickness, and temperature change constitute governing differential equations with variable coefficients. Closed-form solutions to such equations can be obtained only for specific forms of grading functions. For general variations of the properties, numerical methods must be resorted to, and the complementary functions method (CFM) stands as a viable option. Infusion of CFM into the thermoelastic analysis of functionally-graded rotating disks of variable thickness is a unified novel approach; it can efficiently be used for both heat conduction problems and thermal stress analysis. Complementary functions method reduces the boundary-value problem to an initial-value problem, which can be solved accurately by one of many efficient methods, such as Runge-Kutta method. Material models available in the literature for ceramic-metal disks are used in the analysis. First, the proposed solution scheme is verified using simple closed-form solutions for a disk of uniform properties and then displacement and stresses are calculated for nonuniform heterogeneous disks. Use of CFM has given virtually exact results for few collocation points along the radius. Fifth-order Runge-Kutta method (RK5) has been employed as the numerical method.