The temperature distributions within plate or thin tubular fuel elements with bonded end closures are determined with an eigen-function expansion. A one-term approximation is given for end caps longer than the plate thickness. Numerical examples are included for uranium fuel elements with Zircaloy cladding and bonded Zircaloy end caps whose lengths are twice, once, and one-fifth the thickness of the fuel plate. For these examples the ratios of the maximum exterior end cap temperature to the maximum temperature of the fuel material (coolant temperature considered as the base temperature) were 0.38, 0.68, and 0.954, respectively.