Abstract Treating radial cracks by an idealized geometry in fuel elements containing a thermal source gradient, the temperature distribution throughout a cracked fuel element, its gaseous bonding gap, and its surrounding can is found by an approximate series expansion method. This approximation allows the cracked fuel zone to be described by a single series expansion rather than by a multizone approach and allows approximate satisfaction of the boundary conditions at the interfaces of the cracked fuel zone and both at the non-cracked fuel zone and at the can. The method allows for the temperature dependence of the fuel and that of the gas mixture in the cracks and bonding gap, and takes into account the effect of crack openings on gap conductance at the fuel-can interface. The temperature distribution, its mean and variance resulting from the stochastic distribution of radial crack locations, are found. The case of hairline radial cracks, the mean locations of which are azimuthally uniformly distributed, is used to illustrate the importance of cracks on the can temperature distribution and it is shown that their presence may lead to central fuel zone melting problems.