In this article, a unified formulation is presented to analyze the heat conduction and temperature field in a functionally graded thick hollow cylinder. To solve the heat transfer equation in a functionally graded thick hollow cylinder, an analytical method is presented using a nonlinear volume fraction law with variable exponent for mechanical properties. The new unified formulation is obtained based on various thermal boundary conditions such as heat convection at bounding surfaces and constant temperature of bounding surfaces. The functionally graded thick hollow cylinder is considered in axisymmetry condition and infinite length. The temperature field is discussed for various boundary conditions and different grading patterns in functionally graded materials. The presented results and data are verified with published literature.