Nonlinear transient heat conduction analysis is developed for hollow thick temperature-dependent 2D-FGM cylinders subjected to transient non-uniform axisymmetric thermal loads. It is demonstrated here that the temperature-dependency in addition to the material properties variation in the 2D-FGM would lead to highly nonlinear governing equations. To do this, the graded finite element method is employed to model the structures and a quadratic Lagrange shape function has been used to improve the accuracy of the temperature distribution for the two-dimensional heat conduction analysis. Furthermore, time variation of the temperatures and the effects of material distribution variability in two radial and axial directions and the temperature-dependency of the material properties on the temperature are discussed in detail. It is assumed that the material, geometry and volume fraction distribution are axisymmetric but not uniform along the axial direction. According to the results, the variation of the material properties in two dimensions has significant effect on temperature distribution; therefore, it gives more designing flexibility benefits to the designers to implement this kind of material for the thermal barriers purposes.