An advanced method has been developed for the specific purpose of calculating temperatures in fuel element structural analysis. Fuel, cladding, coolant, and structural temperatures are treated by a single system of equations. Melting of the fuel and cladding and boiling of the coolant are included in the model. The method is compared to other solution techniques. The thermal characteristics of the finite element method (FEM) and finite difference method (FDM) transient calculations are compared. The present method includes FDM and FEM algorithms as special cases; an optimum combination of both techniques is the standard usage. Explicit, implicit, or Crank-Nicholson integration procedures are possible. The method is fast running, reliable, and has no stability problems. The new method has been implemented into the temperature calculation subcode system TEMPER for use with URANUS or other fuel element codes. Special attention has been given to user requirements (e.g., an automatic time-step control). The URANUS code, with this subcode system TEMPER, has been applied successfully to difficult fast breeder fuel rod analysis including transient overpower, loss of flow, local coolant blockage, and specific carbide fuel experiments.