The standard analytical approaches to calculating the maximum temperature and surface -heat-flow rate in nuclear reactor fuel plates over-estimates both of these quantities due to the omission of conduction along the axis of the plate. The more general problem, including axial conduction, has been solved for fuel plates in which the clad and meat can be assumed to have the same thermal properties. Calculations made for a natural-circulation reactor show over-estimates of the maximum surface heat flow rate of 4.5 percent and of the maximum temperature rise of 4.8 percent. The error is minimized for systems having a large convection heat-transfer coefficient and will be less than 0.5 percent for most power reactor systems.