This paper deals with a transient thermal stress problem in an infinitely long circular cylinder to which a heated rigid band is bonded in the case where the heat transfer coefficient at the bonded surface is different from the coefficient at the traction-free boundary surface. A finite-difference formulation is used with respect to a time variable for the temperature field because of the difficulty of obtaining an analytical expression. Thus the analytical expression for the temperature with respect to the spatial variables may be obtained. The temperature and stress solutions reduce to a dual integral equation. Coefficients that may be used to determine the strength of the stress singularities are introduced.