In a boundary integral formulation to a thermoelastic problem, the temperature change is treated as an equivalent body force. Therefore, even in the case of no body force acting, the formulation involves volume integrals. In the present paper it is proved that introduction of the thermoelastic potential succeeds in eliminating the volume integrals in the three-dimensional formulation. The formulations are transformed from Cartesian coordinates into axisymmetric coordinates. All the surface integrals are replaced by line integrals along the boundary of the axisymmetric domain. By using the above formulation, the deformation and stress distributions of a bonded cylinder subjected to a uniform temperature change are analyzed numerically.